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Whisk together flour, salt, and yeast in bown of stand mixer
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Whisk water, oil, and sugar together until sugar is dissolved
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With dough hook on low speed, slowly add water to flour and mix until dough starts to form (~2 min)
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Increase speed and knead until dough is smooth and elastic (~8 min)
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Knead dough by hand to form a smooth, round ball (~30 sec). Place in lightly greased large bowl, cover and let rise until doubled (~1.5 hours)
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Press down dough to deflate, transfer to counter and divide into 8 equal sized portions, keeping dough covered with towel at all times
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Shape each dough piece into a rough ball, pinching the seams to keep the dough in place if needed
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Preheat oven to 500F, with a baking stone on lower-middle rack
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Generously flour each dough ball, press and roll into 8-inch round of even thickness
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Let dough rounds rest for 20 minutes
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To bake, transfer 2 dough rounds at a time to baking stone and bake until air pocket is beginning to form (~1 min). Then flip pitas and bake until golden brown (~1-2 min). Transfer baked pitas to a plate and cover with a towel. Let oven rehat for 5 min in between batches
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If dough resists stretching when rolling out, let it relax for 10-20 minutes and then roll again