Make the dough: Combine the water, sourdough starter and whole wheat flour in a large mixing bowl. Stir until the starter is completely dissolved.
75 grams sourdough starter, 226 grams water, 80 grams whole wheat flour
Fold the all-purpose flour into the sourdough starter a third at a time. This will ensure all of your flour is properly hydrated and incorporated into your mixture. Add salt and stir until no dry bits of flour remain and a shaggy dough forms.
240 grams all-purpose flour, 6 grams salt
Knead the olive oil into the dough until it's completely absorbed. Cover the bowl with plastic wrap and let the dough rest in a warm place for 30 minutes.
14 grams olive oil
Knead the dough: Knead the dough in the bowl until completely smooth, about 3 to 5 minutes.
Bulk ferment: Round the dough into a tight ball, cover the bowl with plastic wrap and set it in a warm place until doubled in volume, about 4 to 6 hours.
Pre-shape: Once the dough has risen, turn the dough out on to a lightly floured surface. Divide the dough into 10 portions. Round each ball of dough into a tight ball, set the dough on a heavily floured plate, spaced apart with room to spread.
Cold proof: Cover the plate with plastic wrap and place it in the refrigerator overnight (up to 16 hours).
Prep: If using, place a baking stone on a rack positioned at the very bottom of your oven. Preheat the oven to 500 F for at least 1 hour (or as long as your baking stone normally needs to heat up).
Cut out ten 6-inch squares of parchment paper (this will make rolling your dough out and transferring them to the oven much easier).
Shape: Working with one portion at a time, brush off all the excess flour from the dough. Place the dough in the center of a piece of cut parchment.
Using a rolling pin, flatten the dough out into a 5-inch disc, about ¼-inch thickness.
Set the shaped dough aside, and repeat with the remaining portions. You can stack the dough on top of each other.
Bake: With the parchment paper, transfer the dough to the baking stone. Bake only 3 at a time.
Bake for 2 to 3 minutes or until the pita puffs up, and looks dry and lightly browned. Transfer the baked pita to a serving platter and cover with a dry, clean tea towel.
Enjoy: These pitas are best enjoyed freshly baked.
Store: Store any leftover pitas in a zip-top bag at room temperature for up to 3 days. Reheat the pitas on a dry, preheated skillet for 2 to 3 minutes.