Combine 1 cup warm water, 1 cup sourdough starter and 2 cups flour in the bowl of your stand mixer. Mix with the paddle attachment until completely combined. Let rest 10 minutes.
Add the remaining 1½ cups flour, ¼ teaspoon granulated sugar, 1 ½ teaspoon coarse kosher salt, and 3 tablespoons olive oil to the bowl and switch to the dough hook. Knead for 5 minutes.
Cover the bowl and let it rest for 30 minutes. After 30 minutes, stretch and fold the dough. Repeat the rest and stretch/fold cycle 3 times total.
Cover tightly and place in the fridge overnight - from 12-72 hours.
Remove from fridge and allow to come to room temperature for about 3 hours.
Place a baking stone in the oven and preheat oven to 500 degrees Fahrenheit with a baking stone.
Meanwhile, divide the dough into 8 pieces. Roll each into a ball. Let the rounds rest for 20 min.
Immediately before cooking, roll each piece out into a 6-inch circle. The size is less important than the thickness, aim for ¼" thick.
Place on the baking stone and bake at 500f for 3-5 minutes or until completely puffed and starting to turn golden brown.
Once baked, remove the pita from the oven and wrap them in a clean kitchen towel and slide into a plastic bread bag while rolling and baking the remaining pitas.