I am a bit surprised that District of Pi is listed on Happy Cow. They do offer vegan cheese, but by that measure, you'd have to list most pizza restaurants in DC. Please don't be misled by earlier reviews: Pizza restaurants offering vegan cheese (usually Daiya) is the rule, not the exception in DC. And that's been the rule for years. My favorite is Pete's Pizza, which has a few locations in the area.
You can get the thin crust pizza with vegan cheese at anytime, but it's nothing special. The real reason to go here is the Chicago-style deep dish. And the traditional pizza place atmosphere.
The Chicago style deep dish is really good, and the vegan version does seem to actually be rare. I can't find it when I'm in Chicago. District of Pi and it's original location in St. Louis are the only places I've heard of it.
That said, you must call ahead six hours to request vegan deep dish crust. So do call ahead, they will take your request and your name. Then you show up and let the host/hostess know that you've called ahead. Every single time I've done this, the host has seemed very confused and concerned, and it takes awhile for the staff to identify someone who knows what in the heck I'm talking about. Then eventually they do figure it out, and I have delicious pizza. That said, between calling so far in advance and the kind of bad service, I'm discouraged from going there very often.
If you want pizza and you are in this neighborhood, there is &pizza on E Street near 10th Street, so a block or two away. It's a much more fast food environment, but I prefer their pizza, and it's certainly cheaper.
Updated from previous review on Monday July 20, 2015
Cons: Clueless service, Must call ahead for vegan deep dish,