Roughly mix together the flours, salt, water, olive oil, and sourdough starter in the bowl of a stand mixer.

Mix the dough on a low speed until the mixture is homogenous, then increase the speed to medium-low and continue kneading until the dough transforms into a smooth mass.

For an Ankarsrum mixer, use the dough roller and knead on speed 1-2 o'clock for 8-10 minutes. For a KitchenAid mixer, use the dough hook attachment and knead on a speed 2 for 8-10 minutes.

Transfer the dough to a 2 qt container and let it rest until it fills the container about ¾ of the way, about 10 hours at 70 F (21 C).

Turn the dough out onto a lightly floured counter and divide it into eight pieces, approximately 70-72 grams each.

Shape each piece into a round by tucking all the ends underneath the surface. Cover the rounds and let them rest for approximately two more hours at 70 F (21 C).

Preheat an oven (with a baking stone inside) to its highest setting for at least one hour before baking the pitas.

The oven needs to be very hot in order to ensure all pitas puff. The oven should be at least 500 F (260 C), but the higher the better. I bake mine around 550 F (288 C).

Prepare 8 squares of parchment paper, approximately 6-8 inches wide.

On a lightly floured surface, roll each round out until it is about ¼ inch thick, or 6-inches in diameter. Place each pita on its own square of parchment paper, then cover and rest again while the oven preheats, about 30-60 more minutes at 70 F (21 C).

How to roll: Use two hands, one on either side of the rolling pin, for even weight. Lightly dust the top and bottom of one pita round with flour. Roll the pita forward and back, then give it a half turn and roll it again, forward and back. Next give the pita a quarter turn, repeating the forward and backward rolling motion. Continue giving the pita quarter turns and rolling gently until the pita is about ¼ inch thick and 6-inches in diameter (about three more turns).

After the pitas have had their final rest and the oven is very hot, transfer the pitas to the oven using a pizza peel and bake for about 3 minutes, until puffed and lightly golden. Do not over-bake.

Transfer the pitas to a cloth-lined bowl and cover immediately to reserve moisture.