H Street Great Street has the full scoop. Apparently it's slated to become a gourmet pizza joint called Kith and Kin.
-four potential crust types: whole wheat, regular, nine-grain, gluten-free;
-vegan options (I'm assuming this means Daiya Cheese);
-dine-in or carry-out only.
You can currently secure gourmet pizza at Liberty Tree (1016 H Street), but at one point there were are least three other gourmet pizza places planned for the H Street Corridor. Radius at the Ohio (1380 H Street) is a definite no go. I think that building is for lease right now.
Desperado Pizza, AKA Angelico La Pizzeria, AKA Il Garage, AKA Slice of Life, was slated to open up in the old Sun and Moon building at 1387 H Street. Everything seemed to be moving pretty quickly on this project, and the concept kept evolving, and then it just stopped...abruptly. The same team later announced plans to open a pizza and sandwich shop (called, um, Angelico) at 1421. I haven't noticed any recent action on this one.