1 1/4 t active dry yeast
1/2 teaspoon honey
1/2 cup + 2 T warm water (105–115°F)
1 cups bread flour or high-gluten flour, plus additional for kneading
1/2 cup whole-wheat flour
2 T extra-virgin olive oil
1/2 teaspoon salt
Cornmeal for sprinkling baking sheets
Stir together yeast, honey, and 1/2 cup warm water in a large bowl, then let stand until foamy, about 5 minutes. (If mixture doesn't foam, discard and start over with new yeast.)While yeast mixture stands, stir together flours in another bowl. Whisk 1/2 cup flour mixture into yeast mixture until smooth, then cover with plastic wrap and let stand in a draft-free place at warm room temperature until doubled in bulk and bubbly, about 45 minutes.
Stir in oil, salt, remaining 3/4 cup warm water, and remaining 2 1/2 cups flour mixture until a dough forms.Turn out dough onto a floured surface and knead, working in just enough additional flour to keep dough from sticking, until dough is smooth and elastic, 8 to 10 minutes.
Form dough into a ball and put in an oiled large bowl, turning to coat. Cover bowl with plastic wrap and let dough rise in draft-free place at warm room temperature until doubled in bulk, about 1 hour.Punch down dough and cut into 4 pieces. Form each piece into a ball. Flatten 1 ball, then roll out into a 6 1/2- to 7-inch round on floured surface with a floured rolling pin.
Transfer round to a baking sheet lightly sprinkled with cornmeal. Make 3 more rounds in same manner, arranging them on baking sheets.
Loosely cover pitas with clean kitchen towels (not terry cloth) and let stand at room temperature 30 minutes.Set oven rack in lower third of oven and remove other racks. Preheat oven to 500°F.
Transfer 4 pitas, 1 at a time, directly onto oven rack. Bake until just puffed and pale golden, about 2 minutes. Turn over with tongs and bake 1 minute more. Cool pitas on a cooling rack.
Makes 4 6-inch pitas
Note:Pitas can be baked 1 week ahead and cooled completely, then frozen, wrapped well in foil in a sealed plastic bag. Thaw before reheating, wrapped in foil, 10 to 12 minutes in a 350°F oven.
