Ok, I finally tried this place (the one in downtown), and got myself Khachapouri, which I am told is a Russian comfort food.
If you've never had (or seen) Khachapouri, it's basically an oval shaped pizza-type thing (sort of like a split-open calzone), topped with cheese (feta and mozarella), butter and whatever toppings you would like. I got the one with bacon and ham. All of it was topped with 2 eggs, sunny side up.
Sounds gross, I know, but it was really good. Sort of reminded me of the egg and guanciale pizza at Mozza.
Carl's Jr. has their "breakfast in a bun" hamburger, then this is probably the Russian/Italian equivalent.
Check it out for yourself. https://36pizza.com/?page=42