Add the water, yeast, and 1 teaspoon granulated sugar to bowl. Mix to combine, then let the mixture sit for 5 minutes until it’s foamy.
Add the bread flour, salt, and remaining sugar to the bowl of a stand mixer fitted with a paddle attachment. Mix to combine.
Add the yeast mixture, olive oil, and Greek yogurt to the dry ingredients. Mix on medium speed to combine using a dough hook for 7 to 10 minutes until it’s soft and slightly sticky. Add more flour as needed.
Lightly oil a large bowl and place the pita dough in the bowl.
Cover it with a kitchen towel or plastic wrap, and let rise for two hours until doubled in size.
Preheat the oven to 500 degrees F.
Line two baking sheets with parchment paper.
Turn the dough out onto a lightly floured, clean surface and divide it into 12 equal-sized balls. Cover them with a kitchen towel and let them rise for an additional 20 minutes.
Roll the balls out into circles that are ¼ to ½ inch thick.
Place them on the baking sheets one inch apart.
Place one baking sheet on the center rack of the preheated oven and bake for 7-9 minutes or until puffy and lightly browned on top. *Bake one sheet at a time. Transfer the pitas to a wire rack to cool.