When creating my characters, what I usually consider first is the general type of personality I want my character to have. Then I think of a setting and the history, background of that setting and how it will relate to my character. How did that character come to have the personality that he/she/it has now? The goal I have in mind personality-wise. If it doesn't fit, I form the character to match with that setting. I make a profile skeleton for that character and begin filling it out and taking down notes. I also enjoy selecting meaningful names for my characters, so that also plays a part in how I set them up. Whenever I make a character I tend to try writing for a different personality or perspective.
Anyway, what may help you if none of that above stuff did is that maybe you can try writing that character interacting with another one of your characters. Take a break after, go back to it and read it through. Write for the character alone, thinking to themselves. If you don't want to write them interacting with another character, write an interaction between yourself and the character. Or make up some questions and interview that character.
Another thing you could try, depending on what you like to write, is expanding your awareness or knowledge about history. Go to a library, pick up a few books and see you can find something that catches your interest.
I use an acting method to get characters down. You research, a lot. Make up a backstory. What did they want to grow up to be? Favorite color? Random thoughts during class? What they thought of their teachers in school? Did they even go to school? What about parents? Siblings? Pets? Friends? What kind of people do they like? Dislike? Do they like to drive, or would they rather take a bus or walk? Why? Never stop asking WHY your characters do things. Be their psychologist.
There are so many different aspects of a characters life that you will never be able to get them all down on paper, but the more you get the more you know them. And even then you will still be surprised by your characters when you let them go off on their own.
Last year in my creative writing class we did a n activity that may help you. We wrote down: appearance, job, friends, personality, music, television, culture, food, home place, family and whatever other categories we could think of and then we had to fill out every category to complete the character. From there it is easy to develope the character in the story without the need of a plot up front.
I've been using these things called 'enneagram tests' lately. I take the test in the 'voice' of my characters, making sure to think deeply for each person. Then when I get the results, I read over what type(s) the test said my character was, and dive back into placing these characters in unique situations, using the tests as a guide to fill in any blanks in their personality. But the key is to have these characters interact with each other, as opposed to the environment.
Usually I pick really absurd situations - one that I'm experimenting with now is one of my characters finding out that he's pregnant; he's not surprised, but he finds trouble getting used to how people treat pregnancies in the current area he lives in, which is entirely different from his home culture. Another one is where I consider what would have happened had the 'critical moment' - a bear attack in the middle of a national forest - never happened. In the past, I've had my characters stealing from a bank, dying from a terminal illness, experimenting with each other sexually, fist-fighting each other out of rage, etc... All of these situations are things that would likely not happen in the actual story. They're almost like AUs with the same characters.
Another thing that helps is to imagine your character as a celebrity. First you ask how this would change the character - for example, in my case one of my characters would feel unprepared and terrified, another would probably become boastful and showy, and another would keep cool and try to rally his newfound followers to some noble cause (roughly). Next, you sit them down to an interview and ask them things someone from E! magazine or w/e would ask. While you answer these questions in your character's voice, note how they react. Will they lie? Will they get angry at personal questions? Would they try to act like someone besides themselves?
One other thing is to listen to a whole bunch of songs and think about which of your characters would sing which song. Get ready to get out of your comfort zone for this though - fair warning. You may find yourself thinking about which of your characters is most likely to commit suicide, or something like that. You'll find new scenarios to put your characters in as well.
Yet another tactic that I use is to imagine that my characters are here with me and I'm interacting with them. I've come to the conclusion that one of my characters would outright hate me (I can be rather frivolous, talkative and flighty at times), while the others might be mildly irritated or even just intimidated by the constant stream of words flying out my mouth. Don't become your character for the day (that's highly annoying and ineffective) and don't talk to them out loud (...unless you want to, I guess...) but keep in the back of your mind "Oh yeah, X would do X in this situation!"
Lastly, take all that you've learned through these exercises, and place your character by themselves in a blank room. Look at how they are when no one else is looking. You want this to be different from how they are in the presence of others, because what you are 'in the dark' is the true measure of your personality. Watch them, and see what they do - what they do and why will be one of the traits that motivates your character to act as they do in every situation, and it could be anything from fear, to hatred, to money (and so on).
Besides that, there are lists of "20 things you should know about your characters" and the like. I also consider all my characters' frivolous traits, such as favorite foods and hobbies, because even those can be telling facets of a person's personality. Also, don't forget to do this for your villains/antagonists as well! Even murderous sociopaths need some development TLC - I forget that sometimes.
I am the same as you: I develop my characters' personalities as I go, deciding how they should act in certain situations when they occur. While this is useful up to a certain point, it is also, like you said, a hindrance after a while.
To me, you have this "mature as a writer" thing a bit backwards. Most people go the other way by starting with characters and ending with plot... BUT, I like the fact that you noticed that you are dissatisfied with your writing and are looking to improve yourself. The only thing I can really tell you is to get some experience.
Unfortunately, in order to develop a character, you need a basic plot (at the very least) that you would shape around your characters instead of the other way around. Probably the best practice (if you do Roleplay) is to do a one on one with someone where you guys discuss and plan events outside of the thread so that you can build on the character as you go without shaping it around the plot (because YOU control the plot since it's a one on one). After deciding on the main aspects of a character's personality (like whether they're short-tempered, have a morbid fear of the dark, fall in love easily, etc.) and basic outline for a background (something that you can mold and manipulate without being confined), THEN go to the next stage and choose less important flaws, quirks, traits, and likes and dislikes. Once you have essentially thought up the vague outline of how you want him or her to be, go really in-dept with how their personality will be (See Saffron Bunny's post for reference, but you should really come up with your own points of importance to make a character live up to your expectations).
Back to the RPing advice. While going through the one on one, bring up ideas for events outside of the thread so that you can create a situation where you know exactly what will happen, and you will have time to think about how your new character will act based on the complex (or not so complex) personality that you've just created. After doing this for a while, you will get used to it you will be able to apply it to public RPs without planning ahead.
I went through the same thing. If you want an example, PM me.
BUT, if this isn't about roleplaying, I would suggest starting by thinking of all of the traits that you wish you had (not to be offensive) and choose a few that you think would make a good character. (I used to create the person that I wished I could be.) I see this as the easiest way to start off because you know yourself the best. You know best how you react in situations, how you WISH you reacted in situations (even fictional ones. We all fantasize XD), and how you think in certain situations. BUT, don't forget to give them flaws because flaws are often the most interesting parts of characters. After you develop a persona, try to build on it by adding background (I usually just mix the backgrounds up and change my characters to fit). The most important thing about any character is that you HAVE to stick to their flaws, fears, quirks, etc. For instance, in one of my old RPs dealing with Greek Mythology (leave me alone XD) one of my characters, Kyra, developed a morbid fear of hellhounds because she almost got eaten by one (yes, I know, no comments on the goofiness of it). Well, we had four or five of this particular RP where my character grew up with every new chapter (cause I don't feel like saying RP). In the last one, they went to the Underworld to save her best friend from Tartarus (LONG STORY). While they were down there, they ran into Cerberus and Kyra nearly died of a heart attack even though she had bathed in the River Styx and become an Achillian. BUT I DIGRESS! To be honest, Kyra is my first character and the basis for this advice. That is how I grew to be the writer I am today.
All I can tell you, really, is that you have to figure this out for yourself by experimenting, practicing, and keeping an open mind.
Having a plot driven story is fine even if that plot happens to be the character's growth through A, B, and C events. The best thing to do when you think of a plot is ask yourself A. why is this happening? B. Why do my characters care? and C. How will being involved change my characters?
When it comes to C. it is important to keep in mind that any plot should affect different areas of your character's lives and mentality. It should affect how they view the world, how they view themselves, and inspire in them some sort of change. And what everyone else around them chooses affects your main characters and those supporting characters should likewise have smaller arcs to deal with.
If you're not sure what I mean use a book you know well as an example. I generally use Romeo and Juliet to illustrate. Ask yourself those questions about different characters in the book you're using and sort of see the mentality you should adopt for growth