Hi, effervescenc!
I have very dark brown eyes, too, and during the day I still like to wear eyeshadow, but I stick to more subtle colours.
I use a matte cream/nude colour across the whole eyelid, a shimmery, (very, very) light brown blended into the socket and on to the brow bone and then a very deep purple (blow most of it off the brush!) on a tiny brush into the socket and on the outer corner of the eye. Sounds a bit much, but as long as you don't apply it too heavily and blend it so there are no harsh lines, it'll look lovely. I also use a brown eyeliner for daytime.
Purples (plums, especially), slate blues (be careful of the shade), greys and greens look amazing on brown eyes. You can't really go wrong with brown eyes.
Good luck!