In the bowl of a stand mixer whisk together the flours and yeast. Add the water, olive oil, and honey to the bowl. Fit the mixer with the dough hook and mix on low until all the flour is incorporated. Set aside for 10 minutes.
Sprinkle the salt across the dough and mix on medium speed until the dough forms a smooth, sticky ball that clears the sides of the bowl,. This should take about 8 to 10 minutes. If after 8 minutes the dough is still shaggy, add bread flour, one tablespoon at a time, using up to 2 tablespoons additional flour.
Lightly coat a rimmed baking sheet with vegetable cooking spray. Set aside.
Transfer the dough to a well floured clean countertop and knead for 1 to 2 minutes or until smooth. Divide the dough into 8 equal parts (you can weigh them if you have a digital scale.)
Working with one dough ball at a time, form each into a tight, smooth ball by bringing the edges of the dough together into the center and pinching the seams together to seal. Place the dough balls, seam side down on the prepared baking sheet about 2-inches apart. Repeat until all 8 dough balls are formed. Lightly spray the tops of each dough ball with vegetable spray, then cover tightly with plastic wrap. Refrigerate for at least 16 hours and up to 24 hours.
One hour before baking, adjust the oven rack to the lowest position and set the baking stone on the rack. Preheat oven to 425F.
Remove the dough from the refrigerator. Place one dough ball on a heavily-floured counter, seam side down. Leave the remaining dough balls covered with plastic wrap. Lightly dust the top of the ball with flour then gently press the dough ball into a 5-inch circle using the heel of your hand. Using a rolling pin, gently roll the disk into a 7-inch circle taking care not to crease, fold or bend the dough. Repeat with a second dough ball. Carefully transfer the disks to a rimless baking sheet or peel, knocking off the excess flour. Make sure the side that was facing up when you began rolling, is still facing up.
Slide both the dough rounds onto the hot stone and bake until evenly inflated and lightly browned on the bottom, about 3 minutes. Using a large spatula, turn the pitas and continue cooking until puffed and lightly browned in the center of the second side, about 2-3 minutes. If the pitas do not puff up, turn and bake anyway to prevent burning. Transfer the pitas to a wire rack to cool. Cover lightly with a clean dish towel. Repeat with remaining dough balls.
Store leftover pitas at room temperature in an airtight container. To reheat, wrap the pitas in foil and heat in a 300F oven for about 15 minutes. Pitas are best eaten the day they are made.