If you are in the middle of writing something, or even in the hazy beginnings when something of its form or stuff has surfaced in your mind, ask yourself what questions this project might ask of you, if you will let it. Take ten minutes or two full pages to write in a slow but steady freewrite. If you get stuck or find yourself at the end of the thought, as a further question based on whatever you have uncovered so far.
If you are not in the middle of writing something, perhaps do this exercise for something you have just read, imaginatively taking on the role of the author. What questions do you think this story or essay asked of its author? If those questions were put to you, not relinquishing the author role and returning to answer on your own behalf, what kind of project could you envision that would allow you to answer—or at least ponder—those questions? Take ten minutes or two pages in a slow but steady freewrite to answer first as the other author and then as yourself.