If using active dry yeast - warm the water on low heat up to a max of 110℉ (43℃).Testing with the tip of your finger, it should feel warm, but not hot.If using fresh yeast - keep the water at room temperature water, crumble in the yeast and stir until dissolved.
Mix the bread flour, whole wheat flour and semolina in a stand mixer with a hook attachment set at low speed (or in a large bowl with a spoon.)Sprinklethe active yeast granules on top, then add the water (or pour on the fresh yeast dissolved in water.)
Add the yogurt, olive oil and salt, and mix well on low speed in the stand mixer (or with your hands) until smooth and soft, and all the flour is well incorporated into the dough, about 1 minute (or about 5 minutes by hand.)
First Rise (Dough)
Drizzle the bottom of a large mixing bowl with a teaspoon of olive oil (to prevent sticking). Transfer the dough to the bowl, cover with plastic wrap and let it rise until doubled in volume, about 1 hour.
Second Rise (Dough Balls)
Lightly flour a large surface big enough to work on and let rest 6 dough balls.
Transfer the dough to the work surface and with a dough scraper divide into 6 equal pieces. You can estimate or use a scale (about 5oz, 145g each).
With your hands lightly floured, shape each piece into a ball by pulling opposite sides up from underneath and pinching them together at the top center. Continue from different sides until you have a taut ball. Place smooth-side up, about 2 inches (5cm) apart, on the floured work surface.
Lightly dust with flour and cover with a tea towel. Let rise until doubled in volume, about 30 minutes.
Shape into Pitas
Prepare work area: To avoid sticking while rolling the dough, make sure your work surface is smooth and clean of any dough, then dust it lightly with a mixture of half flour and half semolina.
Flatten into rounds: Gently roll each dough ball back and forth twice (or flatten by hand), then give it a quarter turn and and repeat (lightly flouring the surface whenever the dough starts sticking) until each is 7 to 8 inches (18-20cm) round and ¼ inch (6mm) thick. Drizzle the tops with olive oil.
Cook
Preheat a cast-iron griddle or skillet over medium-high heat until very hot.
Using the palm of your hand (or pancake spatula), flip a flat pita round oiled-side down onto the dry hot skillet. Immediately drizzle the top of the pita (avoiding the pans surface) with olive oil. Cook until bubbles appear and the bottom develops a nice color, about 1 minute. (If bubbles haven't appeared after about 30 seconds, adjust the heat up.)
Flip the pita and cook until golden on the other side, about 1 more minute. (If needed to prevent charring, you can flip the pita a few times. Adjust the heat down if necessary.)
Repeat, stacking the pitas on a wire rack to cool. (If necessary, remove any charred flour from the pan after a few pitas. I use tongs with a damp paper towel.) Serve warm.
Storing
This Greek pita keeps in the freezer so well that I usually double or triple the recipe, and freeze all but today's portion. I highly recommend it. Then thaw and rewarm at your convenience.
At Room Temperature, the pitas stay well for about 2 days. Store in a breadbox or any stainless steel pan with a lid, or a paper bag. Reheat to refresh the texture.
In the Freezer: Freezes well for up to 3 months. If frozen the first day, reheating refreshes the texture beautifully – like freshly made. Take out of the freezer 15 to 30 minutes before reheating.
Reheating
For the best texture, rewarm on a hot dry skillet for about 30 seconds on each side.
Making Ahead
Besides the convenience of freezing cooked pita, you can also refrigerate or freeze uncooked dough balls to continue making later.
Uncooked Dough Balls – Individually wrap the balls in plastic after step 3 of the Second Rise and:
Refrigerate any dough balls that you plan to cook within a day or two. Let them come completely to room temperature before rolling out, by taking them out of the refrigerator about an hour before cooking.
Freeze dough balls for up to 3 months. Let come completely to room temperature before rolling out, by taking them out of the freezer 2 to 3 hours beforehand (or transferring them to the refridgerator the night before, and taking them out about an hour before cooking.