Two vegetarian dishes that are very difficult to find in Japan are ramen and dumplings (gyoza). A chain of restaurants called Chabuton sells both, and they're pretty good. The shop had a location in Akihabara, but it appears to have either closed or moved. The last time I checked, there was still a location in Shimokitazawa.
First you pay for the tickets of the dishes you want.
Plenty of toppings, including sesame seeds and hot sauce. Delicious!