In a small bowl, mix the warm water, yeast and sugar. Cover and let it develop for 10 min.
In a stand mixer with the hook attachment, combine oil, salt, and bread flour until combined.
Add the water/yeast mixture in and mix until the mixture comes together, elastic and smooth (about 8 minutes).
Turn dough out onto a lightly floured work surface and form into a smooth ball. Lightly oil a clean mixing bowl and place dough inside, then rub oiled hands over the top of the dough.
Cover bowl with a damp cloth and let rise in a warm place for 1 1/2 hour.
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 (or set up your pizza oven to 1200F/700C).
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 wooden pallet, pick up each pita and place top side down. (If using a cast iron skillet, bake one or 2 pitas at a time.) Immediately close the oven door and bake until pitas have puffed and are slightly golden around the edges, about 1 minute on each side.
Place baked pitas onto towel-lined plate and wrap with the overhanging towel. Repeat with any remaining pitas.
Bon appétit!