Chef John's Pita Bread
Ingredients:
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1 (.25 ounce) package active dry yeast
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1 cup warm water (90 to 100 degrees F/32 to 38 degrees C)
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1 cup all-purpose flour
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1 ½ tablespoons olive oil
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1 ¾ teaspoons salt
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1 ¾ cups all-purpose flour, or more as needed
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1 teaspoon olive oil, divided