Both are run by the Hare Krishna people and are religious centers rather than eating establishments. But since vegetarianism is part of the doctrine I’ll list them in the Moscow for Vegetarians category..
(1) Metro Botanichesky Sad, ulitsa Selskokhozyaystvennaya 36, korpus 1. As you enter the first thing you see is the photo of our “tandem”. Then a reminder not to leave your things unattended. Dinners served daily but no “official” cafe. Food is bland even by local standards. See http://inveda.ru
YOU CAN BUY VEGETARIAN SAUSAGES THERE.
I PARTICULARLY APPRECIATED FAKE HORSE MEAT
(2) Metro Dinamo, Leningradskoye Shosse 39. A large compound made of metal containers. A semblance of a proper cafe where you can sit and eat. Cold tea and greasy fried potatoes failed to impress me however. Apparently they will be evicted from there soon, possibly to Khimki, or banned altogether.
Sorry to say this tour only contributed to my feeling that vegetarianism and Russia are a mismatch. But do take a look