I went there yesterday with my bf after having heard such a praise from the Chowhound ^-^
We split an order of manti, vareniki with potatoes and mushrooms and khachipuri.
Manti (~$6) were great. They are smaller than how my parents' friend from uzbekistan makes them, but just as delicious: mix of lamb and onions, with a sprinkling of pomegranate powder on top and a little bit of dill.
Varenki (~$5) were also tasty but obviously more delicate and gentle in taste than manti. The feeling had a good proportion of mushrooms so that potatoes didn't dominate, and the dish came w/carmelized onions on top.
I was really looking forward to khachipuri, because I remember having them in Georgia, and really hoping to duplicate that experience. The ones in Stolovaya are done differently (the ones I had in Georgia were half moon in shape with a filling of suluguni cheese and herbs) these had a different pastry shell and were rectangular in shape (almost reminiscent of those greek phyllo pies) and the filling was not as salty as I remember them being. It was still very good and cheesy! and the herbs added flavor into overall creaminess.
As you can tell by this review, i really liked it and so did my bf, the place itself is cute and clean and if you speak russian you will get a kick out of old-school posters above kitchen ("don't dip eggs or fingers into salt!")