Ah, Louise, this is one of those questions that demands an answer of "Yeeessss…"
Once upon a time, the thought of a profile wouldn't've made any sense to me. That was when I pantsed. Now, I'm an extreme plotter. I create backstory and psychological profiles for all my main (and quite a few secondary and tertiary) characters. Where they come from, what they've been through, their conflicts with other characters, the psychological glitches underlying those interactions.
My process is evolving; the current project started without profiles, but it has been rewritten from scratch once already and is coming up on a second from-scratch writing. I have dozens of characters, each of whom has a written-up background, psychological profile, voice (where they are a PoV), appearance, list of relationships, and story arc (ways in which they change). I also, going into this third writing, have an outline that is about 25% of the book's final length.
For my next project (after the other books in this series), I have already started doing something of the same. I have mapped out a very high level plot outline, which has identified who some key characters are: the protagonist, the antagonist, their personal relationship and what they don't know about each other. Now, each layer of plot refinement will trigger a layer of character refinement (or additional character definition), and those character refinements will, it turn, guide the subsequent layers of plot detail. So, yeah, chicken and egg - they develop in parallel.
That's what works for me. But, as I said, extreme plotter.