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1
In a large bowl or in the bowl of a stand mixer, whisk together yeast, honey and 1/2 cup warm water until yeast dissolves. Let the mixture stand 5 minutes until puffy (if it doesn't puff up, discard the whole mixture and start over). Add 1/2 cup bread flour and 1/2 cup whole wheat flour; stir until smooth. Cover bowl with plastic wrap and let it rise in a warm place until doubled, about 45 minutes.
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2
When yeast mixture has doubled in size, add remaining warm water, flours, olive oil and salt. Attach dough hook to the stand mixer and knead on low speed, adding more flour as needed until a smooth, elastic and only slightly sticky dough forms, about 8 minutes. Or if you aren't using a stand mixer, knead dough by hand on a lightly floured surface until a smooth, elastic and only slightly sticky dough forms, about 10 minutes. Shape dough into a ball and place in a lightly oiled bowl; turn once to coat. Cover with plastic wrap and let it rise in a warm place until doubled, about 1 hour.
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3
Punch down risen dough. Divide into 8 equal pieces; shape each piece into a ball. Punch down and stretch each dough ball into a 7-inch wide circle; transfer to baking sheets or a surface lightly covered in cornmeal. Cover with tea towels and let them rise until puffy, about 30 minutes.
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4
Meanwhile, heat oven to 500 F with one rack in the lower third of the oven. Carefully place 4 pitas at a time directly on top of oven racks. Bake 2-3 minutes or until puffy and golden. Using tongs, flip pitas and bake 1 minute more. Transfer pitas to a cooling rack to cool for 2 minutes, then place in a kitchen towel to stay warm and pliable. Repeat with remaining pitas.
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5
Recipe adapted from Annie's Eats and Epicurious.
