Babani's is a quaint, friendly place with simple, light Middle Eastern food. I came for lunch twice and was impressed with the prices (the lunch specials come with a salad and all cost $7-9) and have reasonable portion sizes.
The first time I had a mushroom-zucchini saute (called "bakla"; $8) over white rice which was tasty, though not that unusual or distinctly "Kurdish"---my dish could have been from anywhere between Greece and Iran. I wish they had an option for brown rice, too. However, my friend had a garbanzo stew ($7) with a side of tabouli and both were excellent and far more flavorful than my dish.
The second time I went to Babani's I tried their "niskena" soup ($5 for a bowl) and a side of Kurdish bread ($1.75) which other reviewers had mentioned. The niskena is basically a lentil soup that was fairly tasty, but needed black pepper, as well as some red chili flakes, to really give it some flavor. Otherwise, it's basically a watery, spice-less Indian dal. The Kurdish bread is fluffy, just slightly oily, and goes well with the soup, though be warned it's filling.
On both occasions, the service was prompt, attentive, friendly and knowledgeable about what dishes were vegan (most of the vegetarian dishes are vegan by default, or can be made vegan if you omit the cheese, but none of the appetizers are vegan).
Babani's is definitely a winner.