Whisk flours together.
In a large mixing bowl add water and stir in yeast and sugar until dissolved. Add ½ cup flour mix and whisk together. Place the mixing bowl in a warm place, uncovered, to form a loose “sponge”. Let rest 15 minutes, until mixture begins to bubble.
Add salt, olive oil and most of the remaining flour (keep about ½ cup of the flour for dusting later). Stir until mixture forms a shaggy mass (should be quite sticky, and you can easily pull bits off). 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 flour. Knead lightly for a couple minutes, until smooth. Cover and let the dough rest for 10 minutes, then knead again for 2 to 3 more minutes. The dough should be a little bit moist.
Clean the mixing bowl and coat lightly with extra virgin olive oil. Put dough back in the bowl. Turn the dough a couple times to coat with the olive oil. Cover the mixing bowl tightly with plastic wrap, then cover with a kitchen towel. Put the bowl in a warm place and rest for 1 hour, or until the dough doubles in size.
Deflate the dough and place it on a clean work surface. Divide into 8 equal pieces and shape into balls. Cover with a towel and let rest for 10 minutes.
Using a floured rolling pin (or clean, empty wine bottle), roll each piece into a circle that's 8-9 inches wide and about a quarter inch thick. If the dough springs back, set aside to rest for a few minutes, then continue rolling. Repeat with the other pieces of dough. (Once you get going, you can be cooking one pita while rolling another).
To bake pita in the oven: heat oven to 500 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 baking sheet. Bake for 2 minutes on one side, then use tongs to carefully flip pita over to bake for 1 minute on the other side. The pita will puff nicely when ready. Remove from the oven and cover the baked pitas with a clean towel while you work on the rest.
To cook pita on stovetop: heat cast iron skillet over medium-high heat. (Test by adding a couple drops of water to the skillet, the skillet is ready when the beads of water sizzles immediately). Grease pan with olive oil and wipe off any excess. One at a time, lay a rolled-out pita on the skillet and bake for 30 seconds, until bubbles start to form. Using a spatula, flip the pita over and cook for 1-2 minutes on the other side, until large toasted spots appear on the underside. Flip again and cook another 1-2 minutes to toast the other side. The pita is ready when it puffs up forming a pocket (sometimes, with this method, the pita may not puff or may only form a small pocket. Try pressing the surface of the pita gently with a clean towel). Keep baked pita covered with a clean towel while you work on the rest.