In the bowl of a stand mixer, combine the yeast, honey and 1/2 cup of the water. Stir gently to blend. Whisk 1/4 cup of the bread flour and 1/4 cup of the whole wheat flour into the yeast mixture until smooth. Cover the bowl with plastic wrap and set aside until doubled in bulk and bubbly, about 45 minutes.
Remove the plastic wrap and return the bowl to the mixer stand, fitted with the dough hook. Add in the remaining 3/4 cup of warm water, 11/4 cups bread flour, 11/4 cups whole wheat flour, olive oil and salt. Knead on low speed until the dough is smooth and elastic, about 8 minutes. Transfer the ball of dough to a lightly oiled bowl, turning once to coat and let rise in a warm draft-free place, about 1 - 1 1/2 hours, until doubled in bulk.
Once the dough has risen, transfer to a lightly floured work surface, punch down the dough and divide into 8 equal pieces. Form each piece into a ball. Flatten one ball at a time into a disk, then stretch out into a 61/2-7 inch circle. Transfer the rounds to a baking sheet or other work surface lightly sprinkled with cornmeal. Once all the rounds have been shaped, loosely cover with clean kitchen towels. Let stand at room temperature for 30 minutes, until slightly puffy.
Place an oven rack in the middle position. Place a baking stone in the oven and preheat to 500 degrees F.
Transfer 4 pitas, 1 at a time, onto the baking surface. (Note: These can be baked directly on the oven racks, but best results are baked on a baking stone.) Bake 2 minutes, until puffed and pale golden (mine took longer). Gently flip the pitas over using tongs and bake 1 minute more. Transfer to a cooling rack and let cool completely. Repeat with the remaining pitas. Store in an airtight container for up to 3 days or freeze.
*As always, anything mixed in a stand mixer can be mixed and kneaded by hand.