To make the dough, stir together water, yeast, and sugar in a large bowl until combined.
In the same bowl, stir in 1 cup (120 g.) of flour and olive oil until smooth, breaking up most of the flour crumbs and scraping down the sides of the bowl as needed. Cover with a kitchen towel and let it rest for 15 minutes or until it starts to form bubbles.
Add the other 2 cups (240 g.) of flour and salt. Using a wooden spoon (or clean hands), mix to incorporate until a sticky ball forms, approximately 1 minute.
Cover the bowl with a clean kitchen towel and let the dough rest in a warm place for 30 minutes.
Holding the edge of the dough with your fingertips, fold it over halfway towards the middle. Turn the bowl at 45 degrees and repeat the same process until you complete a full turn. The dough should be smooth and elastic.
Drizzle a teaspoon of olive oil on top, rotate the dough ball, and spread the olive oil to cover the whole thing. Cover and let the dough rest in a warm place until it doubles in size, about an hour.
To prepare the dough balls, dust your work area with a small amount (3-4 tablespoons) of flour.
Transfer the dough and knead it for 30-40 seconds or until it forms a smooth ball.
Using a bench scraper (or a sharp knife), divide the dough into eight equal pieces, about 71 to 74 g. each.
Form each piece into a ball and place them on the lightly floured work surface with the seam sides down. Cover the balls and let them rest for 20 minutes.
To prepare the oven, adjust your oven rack to the lowest position. Place a baking sheet upside down (or a pizza stone) on the wire rack. Preheat the oven to 500 degrees F.*
Cut a large sheet of parchment paper into eight 6 by 8-inch squares.
Using a floured rolling pin, gently flatten each ball into a 6-inch circle. Do not press down too hard so you retain the air bubbles.
Brush any excess flour off before placing them on a square piece of parchment paper. Let them rest, uncovered, for 15 minutes.
You can bake it in the oven or cook it on a cast iron skillet:Using the oven method: To bake the pita, work with two pita rounds at a time, and place the pita loaves with the parchment paper on the hot baking sheet. It is important to work quickly to maintain the oven temperature and allow the pita to “steam” open and create a pocket. Bake for 2 minutes and 30 seconds, flip over, and cook for another 2 minutes and 30 seconds, until lightly golden brown. Remove and repeat this process with the remaining dough.Cooking it in a skillet: Heat a cast iron skillet on medium-high heat for 10 minutes. It should be very hot. Using a brush or paper towel, lightly coat the bottom of the skillet with 1 teaspoon olive oil. Place a pita dough loaf onto the skillet and cook for 1 minute or until bubbles form. Flip and cook for an additional minute. Flip one more time and cook for an additional 30 seconds. Remove from the skillet and repeat until all loaves are cooked. You don't need to add more oil each time, but if the pan starts to look dry, you can add just a little bit more. Serve while they are still warm.