Sougo is one of the few restaurants in Tokyo that prepares shōjin-ryōri (Japanese Buddhist vegetarian cuisine – what the monks eat). Not everything on the menu strictly adheres (it's all good though); if you want the real deal order the shōji-kaiseki (lunch/dinner ¥8000/10,000). Course reservations essential; give them at least two days' notice for dietary restrictions and allergies.
Look for it in the building opposite the APA Hotel.
Also here is Tokyo Cook, offering a variety of Japanese cooking classes in English.