Mix the dry ingredients. In a large bowl, whisk together the all-purpose flour, whole wheat flour, yeast, salt, and sugar.
Keep the salt and yeast from direct contact until mixed to avoid dulling the yeast.
Add liquids and bring it together. Stir in the olive oil and 1 cup warm water (plus yogurt if using). Mix with a spoon until a shaggy dough forms. Add more water, a tablespoon at a time, until the dough holds together and is slightly tacky but not sticky.
Knead until smooth. Turn the dough onto a lightly floured surface and knead for 6–8 minutes, or use a stand mixer with the dough hook for 5–6 minutes.
You want a smooth, elastic dough that springs back when poked.
First rise. Lightly oil a bowl, place the dough inside, and cover with a damp towel or plastic wrap. Let it rise in a warm spot until puffy and nearly doubled, about 60–75 minutes. If your kitchen is cool, give it more time.
Preheat for the puff. Place a baking stone, cast-iron griddle, or an inverted baking sheet in the oven and preheat to 475°F (245°C) for at least 20 minutes.
A very hot surface is key to forming the pocket.
Divide and rest. Turn the dough out onto a lightly floured counter. Gently deflate and divide into 8 pieces for standard pitas, or 10 for smaller ones. Shape each into a tight ball.
Cover and rest for 15 minutes to relax the gluten.
Roll evenly. Working with one piece at a time, roll into a circle about 6–7 inches wide and roughly 1/8 inch (3 mm) thick. Keep the thickness even—this is what helps create the pocket. Dust off excess flour.
Bake quickly. Carefully place 2–3 pitas at a time onto the hot stone or sheet.
Bake for 2–3 minutes until they puff dramatically. Flip and bake for another 1 minute to lightly brown the other side without drying them out.
Cover to keep soft. Transfer hot pitas to a clean kitchen towel and cover. The steam softens them and keeps the texture tender.
Repeat with the remaining dough.
Skillet option. Heat a cast-iron skillet over medium-high until very hot. Cook each pita for 1–2 minutes per side, flipping once the surface bubbles and light spots appear. Press gently with a spatula to encourage puff.