In the bowl of a stand mixer, combine yeast, honey, and 1/2 cup water, stirring gently to blend. Whisk in 1/4 cup whole wheat flour and 1/4 cup bread flour until mixture is smooth. Cover the bowl with a clean kitchen towel and set aside until bubbly and approximately doubled in bulk, about 45 minutes.
Uncover the bowl and add the remaining 3/4 cup warm water, 1 1/4 cups whole wheat flour, 1 1/4 cups bread flour, olive oil, and salt. Using the dough hook, knead mixture on low speed until it is smooth and elastic, 6-8 minutes. Transfer the dough to a lightly oiled bowl, turn once to coat, and let it rise in a warm place for 1-2 hours, until doubled in bulk.
Once the dough has risen, transfer to a lightly floured work surface, punch down, and divide into 8 equal pieces. Form each piece into a ball. Working one at a time, flatten each ball into a disk, and, using a rolling pin, press into a circle about 7 inches in diameter. Transfer the shaped pitas to a piece of parchment paper lightly sprinkled with cornmeal.
Once all the pitas have been shaped, cover them loosely with a clean kitchen towel and allow to rest for about 30 minutes, until they are slightly puffy. Meanwhile, place a baking stone in the oven and preheat to 500 degrees F.
When ready to bake, transfer 1 or 2 pitas at a time onto the baking stone. Bake for 2 minutes, until they are puffed and lightly golden. Use tongs to flip each pita over and bake for 1 additional minute. Transfer to a wire rack to cool. Serve slightly warm or at room temperature, and store in an airtight container.