About 2 weeks ago (pre- Av)we were walking up Amsterdam Ave and came upon Ali Baba. We cannot claim to have discovered it, since it was packed and there was a short feature from New York MAgazine in the window. We had some excellent kebabs -- my wife had cornish hen, and I had beef. The hen was very good, but the beef was outstanding, lighly marinated, perfectly grilled, and juicy and succulent (not adjectives often applied to kosher meat!). With main dishes, you get a pass at their small salad bar -- lots of variations on fried and roasted peppers, and very tasty carrot salad and a vinegary slaw.
It is a Yemenite place, sort of like Mabat out in Brooklyn. The salads weren't as good at Ali Baba, and the menu was smaller and they were out of much of what was listed. But those kebabs! Mine was certainly better than the one I had at Mabat (no mean accomplishment). It is tiny, and mostly for takeout. There can't be seating form more than 8 or 10 people.