It quickly becomes a distant memory. The Gyro Platter at Mr. Gyro’s comes with a big pile of meat, pita bread to stuff it in, tomatoes, onions, feta cheese, olives, a hot pepper and tzatziki sauce.

But it's the extra creamy secret white sauce and notoriously spicy red sauce that made The Halal Guys' chicken and gyro platter a New York legend. The word halal refers to a specific way of ...