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Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In a large bowl, combine the flour with the rest of the ingredients, mixing to form a shaggy dough, about 1 to 2 minutes.
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Transfer the dough to a floured surface and knead until the dough is smooth and springs back to the touch, about 5 minutes. Re-flour your work surface and hands as needed to prevent sticking.
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Place the dough in a lightly greased bowl and allow it to rest, covered, for 1 1/2 to 2 hours. It will relax and become slightly puffy; it may not appear to gain any volume and will not double in bulk.
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Toward the end of the rise time, preheat the oven to 500°F with a rack in the center to upper third. Place a baking stone or steel on the rack to preheat.
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Place the dough on a floured work surface and divide it into eight pieces (about 82g each).
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Gently preshape each piece into a round by pulling the edges in toward the center and pinching them shut to make a tight ball, then turn them over, seam-side down, cover, and let rest for 15 minutes.
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Re-flour the work surface, then roll each piece of dough into a 6" to 7" round, keeping the other pieces of dough covered while you work to prevent them from drying out.
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Place two of the rolled-out rounds onto a lightly floured baker’s peel or an inverted baking sheet. Carefully transfer the rounds onto the preheated baking stone or steel. (Alternatively, if the baking stone or steel is small, bake one pita at a time.)
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Bake for 2 1/2 to 3 1/2 minutes, until pitas have puffed and are set.
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Use tongs to carefully remove the pitas from the oven, then immediately stack them on a clean kitchen towel. Cover with another towel while you bake the remaining rounds.
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Serve the Sourdough Pita Bread warm or at room temperature.
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Cool completely before storing any leftover Sourdough Pita Bread, in an airtight container, for several days; freeze for longer storage.
