In a large mixing bowl add the lukewarm water and stir in yeast and sugar until dissolved. Add ½ cup flour and whisk together. Place the mixing bowl in a warm place, uncovered to form a lose sponge. Give it 15 minutes or so, the mixture should bubble.
Now add salt, olive oil and almost all the remaining flour (keep about ½ cup of the flour for dusting later). Stir until mixture forms a shaggy mass. Dust with a little flour, then knead the mixture inside the bowl for about a minute to incorporate any stray bits.
Dust a clean working surface with just a little bit of flour. Knead lightly for a couple minutes or so until smooth. Cover and let the dough rest for 10 minutes, then knead again for a couple more minutes.
Clean the mixing bowl and coat it lightly with extra virgin olive oil and put the dough back in the bowl. Turn the dough a couple times in the bowl to coat with the olive oil. Cover the mixing bowl tightly with plastic wrap then lay a kitchen towel over. Put the bowl in a warm place. Leave it alone for 1 hour or until the dough rises to double its size.
Deflate the dough and place it on a clean work surface. Divide the dough into 7 to 8 equal pieces and shape them into balls. Cover with a towel and leave them for 10 minutes or so to rest.
Using a floured rolling pin, roll one of the pieces into a circle that’s 8-9 inches wide and about a quarter inch thick. Repeat with the other pieces of dough.
To bake pita in the oven: Heat the oven to 475 degrees F and place a heavy-duty baking pan or large cast iron skillet on the middle rack to heat. Working in batches, place the rolled-out pitas directly on the hot baking sheet. Bake for 2 minutes on one side, and then turn pita over to bake for 1 minute on the other side.
To cook pita on stovetop: Heat a cast iron skillet over medium-high heat. Drizzle a tiny bit of extra virgin olive oil and wipe off any excess. Working with one pita at a time, lay a rolled-out pita on the skillet and bake for 30 seconds, until bubbles start to form. Flip the pita over and cook for 1-2 minutes on the other side.
