Stir together yeast, honey, and 1/2 cup of warm water in a large bowl until dissolved.

Let stand for about 10 minutes until the water is frothy.

Combine bread flour and whole wheat flour in a large bowl.

Whisk 1/2 cup of the flour mixture into the yeast mixture until smooth.

Cover with plastic wrap and let rise in a warm, draft-free area until doubled in bulk and bubbly, about 45 minutes.

Stir in olive oil, salt, remaining 3/4 cup warm water, and remaining flour mixture into yeast mixture until a dough forms.

Knead dough on a floured surface (or with a Kitchen Aid mixer), adding just enough additional flour to form a smooth elastic ball, about 8 minutes.

Form dough into a ball, transfer to an oiled large bowl, and turn to coat with oil.

Cover with plastic wrap and let rise in a warm, draft-free place until doubled in bulk, about 1 hour.

Lightly sprinkle cornmeal on two baking sheets or pizza peel.

Once doubled, punch down and cut into 8 pieces.

Flatten each piece into a ball on a floured surface, then roll out into a 6 1/2 to 7 inch round.

Transfer rounds to baking sheets sprinkled with cornmeal.

Cover with non-terry cloth towels and let stand at room temperature for 30 minutes.

Place baking stone (or cookie sheet) on a rack in the lower third of the oven and preheat oven to 500°F.

Transfer 4 pitas, one at a time, to the preheated baking stone (or bake directly on the oven rack).

Bake until puffed and pale golden, about 2 minutes.

Turn over with tongs and bake for 2 minutes more.

Cool pitas on a rack for 2 minutes, then stack and wrap loosely in a kitchen towel to keep warm.

Bake each circle for 4 minutes until the bread puffs up.

To Freeze baked pitas wrap in foil, place in a sealed plastic bag and seal, and freeze. Thaw, still wrapped, before reheating. Heat wrapped in foil for 10 - 12 minutes in a 350°F oven.