There is a restaurant chain called Olga's that makes gyro sandwiches. Their pita bread is cooked fresh--or, at least it used to be, things change. But the bread was soft and did not have a pocket. They serve the fillings in the folded over bread. I don't know if this is authentic to middle eastern cuisine, but it is delicious. Does anyone have a similar recipe for this kind of bread?
(Oh, and $10 off your order of $50 or more in the Food52 Shop, too.)