Activate yeast mixture:

In a large bowl, combine the sugar and yeast by whisking, then pour in the warm water and mix. Allow the mixture to sit for about 5 minutes until it becomes frothy, indicating the yeast has activated.

Mix dough ingredients:

Mix in the salt and olive oil. Using a wooden spoon, incorporate 2 ½ cups of flour. Keep stirring, adding flour one tablespoon at a time, until the dough begins to separate from the bowl's sides.

Knead dough until elastic:

Lightly flour a work surface with some of the leftover flour. Transfer the dough to the floured surface and knead for 15 minutes until it is smooth, soft, and elastic. (If using a stand mixer with a dough hook, knead for 10 minutes.) Sprinkle additional flour as needed to prevent sticking, but avoid adding too much, which can make the dough tough. The dough should feel tacky but not overly sticky.

Oil and return dough:

Fold the edges of the dough inward, then grease the same bowl with olive oil. Place the dough back in the bowl and turn it to coat evenly with oil.

Let dough rise:

Cover the bowl with plastic wrap or a clean kitchen towel. Let the dough rise in a warm spot for about 1 hour, until it has doubled in volume. To test, press two fingers into the dough; if the indentation remains, it is ready.

Divide and shape balls:

Take the dough out of the bowl and divide it into 10 equal portions, each weighing roughly 2 oz (57g). Shape each portion into a ball by tucking the edges underneath, then cover with a towel and let rest for 20 minutes.

Roll pita disks:

Using a rolling pin, flatten each dough ball into a disk about ¼-inch thick (approximately 6 inches in diameter). Imperfect shapes are fine; aim for the best circle or oval possible.

Preheat skillet and rest:

Allow the raw pita disks to rest for 5 minutes while you preheat a large cast iron skillet over medium heat. Lightly oil the pan, then place one pita in the skillet.

Cook pita first side:

Cook for 20 to 30 seconds until 4 to 5 bubbles appear on the surface, then flip and cook for another 20 seconds. Flip once more and cook for 1 minute, allowing the bread to puff.

Flip and puff pita:

Flip again to encourage further puffing, then remove from the pan and cover with a towel to retain steam and keep the pita soft. Repeat with the remaining pitas. Not all will puff dramatically, but they should develop large bubbles. Wrap finished pitas in foil to keep warm.

Bake pitas in oven:

For oven method: Preheat a pizza stone or large cast iron skillet in the oven to 475°F (245°C). Brush with olive oil and place as many pitas as will fit without overlapping. Bake for 2 minutes on one side, then flip and bake for 1 minute more.