In a small bowl or measuring cup, whisk together lukewarm water and active dry yeast. Allow to proof for about 5-10 minutes, until foamy.
In a large mixing bowl or the bowl of a stand mixer, mix together all-purpose flour, salt, and granulated sugar.
Pour the foamy yeast mixture into the dry ingredients along with the olive oil. Mix by hand, or with the paddle attachment of the stand mixer, to form a shaggy dough.
If working by hand, turn the dough out onto a lightly floured surface and knead for 8-10 minutes. If using a stand mixer, switch the paddle out to the dough hook and knead for 6-8 minutes. Work in extra flour a few tablespoons at a time, only as needed, to achieve a smooth and elastic texture.
Form the dough into a ball. Lightly grease the mixing bowl with olive oil and add the dough, giving it a flip to evenly coat it with oil. Cover and allow to rise for about 1 hour or 1 ½ hours, until roughly doubled in size.
Turn the risen dough out onto a clean work surface and divide it into about 6-7 portions. Shape each portion into a ball by tucking all its edges toward the center, then pinching them together. Repeat for all remaining dough pieces, place the balls seam-side down. Cover with a damp cloth or plastic wrap and allow to rest for 20 minutes.
If you will be cooking your pitas in the oven, begin preheating your oven to the hottest temperature at this point.
Roll each dough ball out into a disk about 6" in diameter. Use flour on your work surface and rolling pin as needed to prevent sticking.
Allow the rolled-out dough to rise for another 20-25 minutes, until lightly puffy.
To transfer the rolled-out pita bread you can use a pizza peel, a cutting board, or another cookie sheet without a lip. Gently load one pita bread at a time onto the peel and carefully slide it onto the pizza stone.
Immediately after transferring the pita into the oven, close the door and allow them to cook for 3-5 minutes.
Heat a clean, dry cast-iron skillet over medium-high heat for about 5-8 minutes prior.
Gently lay the uncooked pita bread in the center of the preheated skillet. Let it cook for about 1 minute on the first side.
Carefully flip the pita bread to the second side. Cook on the second side for about another minute.
I recommend keeping the cooked pitas covered with a clean kitchen towel.
