SOLVED. Adult fiction. Multiple references to the Moon throughout the story. Cover: beige/dark with moon shining in the middle. Remember the ending. Spoilers ahead. [s]

[Barbara]

Is it fantasy? Moonflash, by Patricia McKillip might be it.

[Stella]

"The girl who drank the moon" might be it

[Kris]

Glad you found your book, Edvin. Here's the link - Moon Palace by Paul Auster.