Moustache Pitza Restaurant is rated by "Where the Locals Eat" as the BEST MIDDLE EASTERN in New York City -2009 rating A step up from hole in the wall but obscure enough to pat yourself on the back for finding it, Moustache serves up some of the freshest jazzed-up versions of Middle Eastern classics around.offer out-of-the-oven pita bread and a version of baba ghanoush that defines the dish like Project Runway defines style.