A good recipe for pita bread requires preparing a yeast dough, letting it rise, patting it down, forming balls for the second rise, and flattening the dough before cooking in an oiled cast iron skillet. Prepare the dough by mixing 1 package active dry yeast with 1 cup lukewarm water and 1 cup flour in the mixing bowl of a stand mixer. Allow the mixture to sit for 20 minutes to create a sponge. The mixture should foam and bubble.
Add 1 1/2 tablespoons olive oil, 1 3/4 teaspoons salt and 1 3/4 cups flour to the bowl, and mix using the dough hook to form a soft, sticky dough. Add a little more flour if necessary to keep the dough from sticking to the sides of the bowl. Set the mixer to low, and allow it to knead the dough for five to six minutes. Add 1/4 teaspoon olive oil to the bowl, and turn the dough to cover it in oil. Cover the bowl with foil, and allow the dough to rise for two hours.
Pour some flour on the countertop to prevent the dough from sticking, and dump the contents of the bowl onto the flour. Pat the dough into a flat shape about 1 inch thick. Cut the dough into 8 equal pieces, and form each piece into a ball. Allow 30 minutes for the dough to rest. Flatten each piece to a thickness of 1/4 inch before cooking in the skillet.