While the dough is resting, preheat the oven to 450°. If you have a baking stone, put it in the oven to preheat as well. If you do not have a baking stone, turn a cookie sheet upside down and place it on the middle rack of the oven while it is preheating. This will be the surface on which you bake your pitas.
After the dough has relaxed for 20 minutes, spread a light coating of flour on a work surface and place one of the balls of dough there. Sprinkle a little bit of flour on top of the dough and use a rolling pin or your hands to stretch and flatten the dough. You should be able to roll it out to between ¼ – 1/8” thick – 6 inches in diameter. If the dough does not stretch sufficiently, you can cover it with the damp towel and let it rest 5-10 minutes before trying again.
Place discs on a lightly greased baking sheet or parchment paper and let rise, uncovered, until barely doubled in thickness, about 30-45 minutes.
Open the oven and place as many pitas as you can fit on the hot baking surface. They should be baked through and puffy after 3 minutes. If you want your pitas to be crispy and brown you can bake them for an additional 3 to 5 minutes, but it isn’t necessary.