Greece has a “pita culture” and the round or oval flatbread that most non-Greeks instantly think of when hearing “pita” is just a small part of it. Greek pita can refer to one of two dough products. One is the flatbread used for scooping up an assortment of appetizing dips and for wrapping many Mediterranean sandwiches like gyros, souvlaki and falafel. Perhaps more importantly to Greeks, pita also refers to a phyllo-based pie. Pites, the savory or sweet phyllo pies that most Greeks think of when they hear pita, or mean when referencing them, come in many varieties. My intention in starting the pita challenge was not only to nail…