Everyone has a different process how they manage their project, so here is my (i think) rather unorthodox method on how to be brainstorming and working at the same time.

Disclaimer: I make only story driven puzzle games, so maybe this method is not for everyone.

1) I always start with GRAPHICS, yes, you read it right. The thing that should be done last. The main reason is, that my main focus is the story/dialogue, and instead of just sitting over a white piece of paper thinking about story, I start drawing out of my head, whatever comes to my mind. And while drawing, my mind goes towards these places I draw. I make up some scenes, characters, items, locations, time periods, etc. and it helps me imagine these situations better.

So it goes something like this "I'm in a mood for some steampunk environment... This looks like a lab, I like it. So there will be these two professors... No, a professor and a student. The professor comes up with an idea and the student (you) must help him. There will also be some alchemy related puzzle..." There you go. You have a story right there!

2) After graphics (and ideas) are done, I start writing specific dialogues and puzzles

3) Implementing graphics, puzzles and coding. Finishing game.

Pic.: My previous game Homunculus for reference.