Most houses in the southwest have built in designs that, to a lot of us, seem pointless or like a waste of space. In this case the shallow recess in the wall has left me asking, why? You can add a little character and texture when you fill the space with wood. Then hang pictures, signs, mirrors, or other decor.
Lowes sells packages of inexpensive pine boards, and is what was used in this project. The only difference is that we flipped the boards so the rough side was face out instead of the smooth. Another option is to forgo the wood and hang a custom mirror to fit the full space.