Even in Baghdad by the Bay, it takes guts to identify yourself as an Iraqi restaurant and not hide behind the one-size-does-not-fit-all rubric of Middle Eastern. Visit Baghdad Nights in the lower Haight and you'll be rewarded by a cozy setting, very caring service, and a menu that includes not only such expected dishes as falafel, shawarma, and a variety of kebabs, but also uncommon homey specialties. The Iraqi maza — cold appetizer starter plates including falafel, hummus, baba ghanoush, and several other dips, with assorted pickles, and available in two sizes — serves more than the two or four indicated. The restaurant bakes its own unusually airy bread. Try the tabsi (a mild ground lamb and beef curry) or a beraini (stewed beef or chicken with almonds, raisins, and garbanzo beans, served on rice with yogurt sauce) to follow, or one of the three succulent stewed lamb shank preparations. The baklava sampler plate and rosewater-scented pistachio custard are a step up from the standard issue. Belly-dancing on Friday and Saturday nights.