Meanwhile, place a baking steel or 12-inch cast iron skillet on the top oven rack and preheat oven to 500°F (260°C). Line a plate with a large, clean kitchen towel and set aside.
Punch down the dough, transfer to a lightly floured work surface, and cut into 6 even pieces. Form each dough piece into an even ball. Cover with a damp towel and let rest for 10 minutes.
Roll each piece of dough into about a 7-inch circle, no more than 1/4 inch thick, taking care not to tear dough and keeping the thickness even all around. Place dough disks on a lightly floured surface, cover with a damp towel, and let proof until slightly puffy, about 30 minutes.
Working with as many pitas as will fit on the steel at once, pick up each pita and place on the steel top side down. (If using a cast iron skillet, bake one pita at a time.) Immediately close the oven door and bake until pitas have puffed and are slightly golden around the edges, about 3 minutes. Be careful not to over-bake.
