Here is our family recipe:
PITAS
Sponge:
7g Yeast
125g All-purpose flour
250g warm water
Combine and let the sponge rest for about 20 mins at room temperature.
In a stand mixer bowl combine:
1 sponge from above
1 1/2 Tbsp Olive oil
2 tsp fine sea salt
220g All-purpose flour
Knead with the dough hook for 5-6 minutes on low, adding a little more flour as required. You want the dough to pull away from the sides and basically have everything in a ball on the dough hook and nothing but residual oil on the sides.
Wipe inside of bowl with 1/4 teaspoon olive oil. Turn dough around in bowl to cover with a thin film of oil; cover bowl with foil and let sit until dough has doubled in size, about 2 hours.

Remove dough from bowl and place onto a floured work surface. Lightly pat into a flat shape about 1 inch thick. Use a knife to cut dough into 8 pieces.

Form each piece into a small round ball with a smooth top, pulling dough from the sides and tucking the ends underneath the bottom.

Cover dough balls with lightly oiled plastic wrap and let rest for 30 minutes.
Sprinkle a small amount of flour on a work surface and top of a dough ball; gently pat dough ball flat with your fingers, forming a flat, round bread about 1/4 inch thick. Let dough round rest for 5 minutes. Repeat with remaining dough balls.

Brush a cast-iron skillet with remaining 3/4 teaspoon olive oil and place over medium-high heat. Lay pita bread into hot skillet and cook until bread begins to puff up and bottom has brown spots and blisters, about 3 minutes. Flip, cook 2 more minutes, and flip back onto original side to cook for about 30 more seconds. Pita bread will begin to puff up and fill with hot air. Stack cooked breads on a plate; when cool enough to handle, break breads in half and open the pocket inside for stuffing.