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1
Place 1/2 cup of the water in a small bowl and stir in the honey to dissolve.
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2
Sprinkle the yeast over the top and stir until the yeast is dissolved.
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3
Let stand until foamy, about 5 minutes.
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4
In a stand mixer fitted with the dough hook, mix the flours, salt, and the 3 tablespoons olive oil together.
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5
With the mixer on low speed, add the yeast mixture, then gradually add the remaining 1 1/2 cups water and mix until the flour is completely integrated.
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6
Knead dough on a lightly floured board for about 5 minutes, or until smooth, elastic, and no longer sticky, dusting with flour as needed.
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7
Place the dough in an oiled bowl and oil the top of the dough lightly, then turn the dough to coat it with oil.
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8
Cover with a damp towel or plastic wrap and let rise in a warm place until doubled in size, about 1 hour.
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9
Prepare a very hot fire (500F) in a wood-fired oven or cooker, or prepare a hot indirect fire in a wood-fired grill.
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10
If using a conventional oven, place the oven rack in the lowest position.
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11
Turn the dough out on a lightly floured board and knead to remove the air bubbles.
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12
Roll into a log and divide the dough evenly into 12 pieces.
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13
Form each piece of dough into a ball, and then use a rolling pin to flatten into disks about 1/4 inch thick and 6 inches in diameter.
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14
Place the disks on a lightly greased baking sheet and let rise, uncovered, until almost doubled in thickness, 30 to 45 minutes.
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15
Bake on the baking sheet or grill over indirect heat until puffed and lightly golden, 5 to 10 minutes.
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16
Remove from the heat and let cool on wire racks for 5 minutes.
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17
Cut each pita into a half circle and separate on the cut line with a fork to create a pocket.
