Thanks to Go Dairy Free viewer Tara for emailing this recommendation.
This is a vegetarian restaurant that is primarily vegan. As noted by a reader below in the comments, they may have dairy milk available, but the menu appears to be mostly, if not completely vegan-friendly (dairy-free!). Their menu also notes which items are raw, gluten-free, and/or soy-free. They offer a varied menu (see website), but it is generally a casual eatery with soups, sandwiches, bowls, and more.
Locations: They offer two locations, one in the U-District and one in West Seattle. See their website below for locations, hours, and phone numbers.