Whisk flour and yeast together in the bowl of the stand mixer. Add ice water, oil, and honey on top of the flour mixture.
With a dough hook, mix at low speed until all of the flour is moistened, 1 to 2 minutes. Let dough stand for 10 minutes.
Add salt to the dough and mix on medium for speed until the dough forms a satin and sticky ball that clears the sides of the bowl. Approximately 6 to 8 minutes.
Transfer dough to a lightly oiled surface and knead until smooth, approximately 1 minute. Divide dough into 6 equal parts
Shape dough pieces into tight and smooth balls. Transfer, seam side down, to a rimmed baking sheet coated with oil spray. Spray top of dough balls with oil spray.
Cover tightly with plastic wrap and refrigerate for at least 16 hours and ideally 24 hours.
One hour before baking pitas, adjust baking rack to the lowest position. Set baking stone on rack and heat oven to 450F.
Remove dough from refrigerator. Coat one ball generously with flour and place on well floured surface, seam side down.
Use the heel of your hand to press ball into a circle. Using a rolling pin, gently roll to a 6 to 7 inch circle, adding flour as necessary to prevent sticking. The pita should be a quarter inch thick.
Repeat with 2nd dough ball and use a pastry brush to remove excess flour. Transfer pita rounds to a wooden peel, making sure the seam side is down.
Slide both pita rounds carefully on to the baking stone and bake for 2 minutes. Flip pitas (they will not be fully browned).
Bake until puffed and lightly browned in the center of the second side, approximately 2 to 3 minutes.
Transfer pitas to a wire rack to cool, covering loosely with a clean towel.
Repeat shaping and baking the remaining dough balls.
Let the pitas cool 10 minutes before serving.