Yield: 12 pieces
1. Pour ½ cup of water into the bowl of a stand mixer. Sprinkle the yeast evenly over the water and let it bloom for a few minutes then whisk until smooth. Whisk in the sugar to dissolve. Whisk in ½ cup of flour to form a loose paste. Cover the bowl with plastic and let it rise in a warm place until the mixture has risen and is bubby, about 15 minutes.
2. Mix together the remaining flours and salt.
3. Add the remaining 1 cup of water to the bubbling yeast mixture and then the flours and salt. Use a dough hook to knead the bread until it is smooth and elastic, about 10 minutes.
4. Coat a large bowl lightly with oil and place the dough in the bowl. Flip the dough over to coat it on all sides. Cover the bowl with plastic wrap and allow to sit in a warm place for 2 hours or until it has doubled in size.
5. Punch down the dough, turn it out onto a lightly floured counter and roll it into a thick log. Cut the log into 12 equal pieces and roll them into balls. Let the balls rest on the floured counter or on a lightly floured sheet pan, covered lightly with a damp cloth or piece of plastic wrap, for 10 to 15 minutes. The balls will start to rise and press on the plastic wrap. Once they do they are ready to roll.
6. Preheat the oven to 500 degrees F or as hot as it will go. Position a rack on the lowest rung in the oven and remove the racks above for easy access. Place a half sheet pan on the newly positioned rack to preheat.
7. Use a rolling pin to roll each ball into a circle 5 to 6 inches in diameter and ¼-inch-thick. The pita will stick slightly to the counter. Do not flour the counter or the dough will slide around and it will be difficult to roll the rounds thinly. Let the pita rest for 5 minutes before baking.
8. Spread your finger out with your palm facing upwards and lay the pita over the top. Open the oven door and flip your hand over to drop the pita on the hot sheet pan. Immediately shut the oven door and do not open it until it is time to flip the pita after it has puffed. This should take about 3 to 4 minutes. Reach into the oven and flip the puffed pita with a pair of tongs. Cook for 2 minutes more. Remove the pita from the oven and place it on a clean dish cloth or napkin and cover it. Press gently on the pita with the closed tongs to deflate it. Mind the steam from the deflating pita as it is very hot and quite a shock when it hits you. Repeat for the remaining pitas. Store the warm pitas in a napkin lined basket for serving. You can also cool the pitas and keep them sealed in a zip lock bag in the fridge or freezer. Thaw and rewarm before serving.