I was so excited to find this. I made Chicken gyros and the homemade pitas where what made them so delicious. Remember not to let the dough dry out while they are resting and waiting to be put in the oven, otherwise they will not have that puff you want when you bake them.
1 Tbs instant yeast
1 1/4 cups warm water
1 tsp salt
3 to 3 1/2 cups all-purpose flour
In the bowl of a stand mixer or in a large bowl (if mixing by hand), combine the water, yeast, salt and 1 1/2 cups flour. Beat to form a soft batter-like consistency. Add additional flour until the dough starts to come together. Add enough flour to form a soft dough that clears the sides of the bowl (but is still slightly tacky to the touch) and knead for 4-5 minutes with an electric mixer or 8-9 minutes by hand until the dough is smooth and elastic.
Turn the dough onto a lightly floured countertop and divide the dough into six equal pieces. Roll the dough pieces into a ball shape. Lightly cover the balls of dough and let them rest for 10-15 minutes. Roll each dough ball into a thin disc, about 1/4-inch thick. Do your best to keep an even thickness throughout the entire disc of dough since this helps the dough puff in the oven. Let the pita rounds rest, lightly covered, for 30-40 minutes until they are slightly puffed.
While the pita rounds are resting, preheat the oven to 425 degrees F. When the pitas are done resting, gently flip two of them onto a large, rimmed baking sheet lined with parchment paper. Make sure you flip them so the side that was resting on the counter is now facing up. Spritz with water, if needed.
Bake the pitas for 10 minutes, until they are starting to brown very lightly on top and they have puffed several inches high. Keep in mind, though, that it won't be unusual to have some pitas that just refuse to puff. Still take them out after 10 minutes - they will make great flatbreads and will still taste delicious even if they don't have the magical pocket inside. The trick to great pita puffing is to roll the pita evenly and to make sure the dough isn't dry on top when it goes in the oven (hence the reason for flipping the pita onto the baking stone or baking sheet). Don't get discouraged if your pitas don't all puff. The baked and cooled pitas can be frozen or stored covered at room temperature for 1-2 days.