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1
Combine flour, yeast, and salt in a large bowl. Add the oil to the warm water, pour into the dry ingredients, and mix to a shaggy dough. Turn onto a lightly floured surface and knead for 8–10 minutes until the dough is smooth, supple, and springs back when pressed with a finger.
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2
Return the dough to the bowl, cover, and leave to rise at room temperature until doubled in volume.
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3
Place a baking stone or the heaviest steel pan available on the highest oven rack. Set the oven to its maximum temperature — 280 °C in a home oven — and preheat for a full 45 minutes. The stone or pan must be at full radiant heat before a single pita is placed on it.
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4
Divide the dough into six to eight equal pieces. On a lightly floured surface, roll each piece to a disk of uniform 4–5 mm thickness. Uniformity across the entire disk is essential; thick patches will not puff. Cover the rolled disks and rest them for 10–15 minutes. A pita that is unevenly rolled, placed on an insufficiently preheated surface, or moved directly from rolling to the oven without resting will not puff — and a flatbread without a pocket is not pita.
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5
Slide one or two rested disks directly onto the preheated stone or pan. Bake for 2–3 minutes. The dough will balloon into a full sphere within the first 90 seconds as steam separates the two layers. Remove when the pita is pale gold and fully puffed; do not allow it to brown and crisp.
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6
Transfer the baked pitas to a single layer on a clean surface and leave uncovered for 5 minutes before stacking. Do not stack immediately: trapped steam produces a leathery exterior. After 5 minutes the pitas may be stacked and covered with a cloth to retain their soft, pliable character.