Brasserie Beck, on 11th Street, NW:
We've eaten there several times. The staff is very nice about checking for soy if they're not sure. They use canola oil to make their Pommes Frites, which are thin and sprinkled with salt and dried parsley, and served with a trio of house-made flavored mayonaises. The three flavors are garlic, tomato, and curry--and the mayo is made with canola oil, too!
Pete's New Haven Style Apizza (2 locations, and soon to be a third across the river in the Clarendon section of Arlington):
"Apizza", pronounced ah-BEETS, is a dialectical word for pizza, and it's used in the New Haven, Connecticut area. (If you want to read about New Haven-style apizza, go to the Wikipedia page here; it is a good explanation.) I emailed Pete's Apizza and asked about their pizza--it is made with pure olive oil and their sauce is house-made and also soy-free. We ordered sausage and mushroom and it was heaven. Make sure to try the Foxon Park white birch beer; they get it shipped from East Haven, Connecticut, where it's made and bottled. (I grew up in East Haven and the next town east from there, North Branford, and I vouch for the authenticity of the apizza and love the soda.)
I can't vouch for the rest of the menu, but they were nice to me when I asked about the pizza, so I have high hopes for the other menu items also.