It is rather uncommon in Japan to be vegan I guess because everyone was supprised I did not eat meat nor dairy. :) So I searched online and found this information on HappyCow. It is a very nice place, the staff were communicative (contrary to all the other restaurants I have been to in Sapporo) and helpful. The dish was delicious and unlike all the other places, they served brown rice instead of white one. It wasn't so greasy as everywhere else (I would call everything that I was served before an oil soup :P). I took some muffin with me when I left. I definitely recommend this place.
They are usually closed on Thursdays. I was lucky they were open as an exception this time. :)