Put 1 cup water in your stand mixer bowl. Stir in the honey.
Sprinkle yeast over water, mixing in lightly. Let stand about 5 minutes to develop a foam.
Add remaining water, oil, salt, and 3 cups of flour. Mix on low speed.
Add remaining flour, continuing to mix on low speed.
Knead on medium-low speed for 5-7 minutes, or until the dough forms a soft ball and pulls away from the sides of the bowl.
Place in a greased bowl. Cover and let rest in a warm place for about 1-1½ hours, until doubled in size.
Punch down. Cover and let rest for 10 minutes.
Divide into 12 equal pieces. Form each into a ball.
Knead each ball for about one minute. Cover and let rest for 20 minutes.
Prepare baking sheets with grease. Sprinkle cornmeal over the grease.
Roll each ball into an 8-in. circle. Place on prepared baking sheets.
Cover and let rise in a warm place until doubled, about 30 minutes.
Preheat oven to 475°F
Bake pitas 8-10 minutes or until browned. Pita will puff as they bake.
Remove from pans and cool on wire racks.