Order dolma at Iraqi House, and you submit, happily, to chance. What arrives might be whole onions or green bell peppers, or eggplant, or tomatoes, their insides emptied to make way for a meld of ground lamb and basmati rice, tinged by tomato, with vivid threads of parsley and dill running through.

Here, too, will likely be grape leaves as big as your palm, blanched and rolled round the same lamb and rice, making plump stubs like half-smoked cigars. The leaves are fairly constant, the other vegetables more unpredictable.

“Every dish is different,” said Mohammed Almandalawi, who opened the restaurant in July. “It depends on the luck of the person.”

Mr. Almandalawi was born in Mississippi, the son of Iraqi immigrants who decided to return to Baghdad after the first Persian Gulf war and later settled in Qatar. A former competitive swimmer, he moved to Bay Ridge, Brooklyn, last fall and staked a claim on this plain-spoken storefront, recently vacated by a rotisserie chicken joint, with Chinese chow fun to one side and tacos and margaritas to the other.