In a large mixing bowl, combine the warm water, yeast, and 1 teaspoon of sugar. Stir gently, then let it sit for 5 minutes, or until the mixture becomes foamy.

Add the bread flour, salt, remaining 1 tablespoon sugar, olive oil, and Greek yogurt to the yeast mixture. Stir until the dough comes together.

Transfer the dough to a lightly floured surface and knead for 7–10 minutes, or until smooth and elastic. Lightly oil a clean bowl, place the dough inside, and cover with a towel or plastic wrap. Let rise in a warm spot until doubled in size, about 2 hours.

Preheat oven to 500°F (260°C). Line two baking sheets with parchment paper.

Punch down the risen dough and turn it onto a clean surface. Divide into 12 equal pieces and roll each into a ball. Using a rolling pin, flatten each ball into a circle about ¼–½ inch thick. Arrange them on the baking sheets, leaving space between each.

Bake one sheet at a time until the pitas puff up and turn lightly golden on top. Begin checking at 5 minutes — they typically take about 8 minutes. Rotate the pan halfway through baking for even browning.

Transfer baked pitas to a wire rack. Serve warm or store for later use.