Step 1In a large bowl, mix together the all-purpose and whole wheat flours, then stir in about 3 cups water. Set aside to rest for 30 minutes. Don’t worry if the dough seems a little dry. In a separate bowl, combine the yeast, sugar and remaining water and also set aside to rest for 30 minutes. The yeast mixture will become frothy and look like a sponge.
Step 2Combine the yeast mixture with the dough and the salt and mix until smooth, 2 to 3 minutes. Set aside to rest for another 30 minutes.
Step 3Using a bench scraper or your hands, fold the dough over itself 4 to 5 times (this builds structure), then set it aside to rest for another 30 minutes in the same bowl.
Step 4Turn the dough out onto a lightly floured surface and portion the dough into 12 pieces (about 5 to 5½ ounces). Using both hands and a little flour (not too much), round the pieces tightly and place on a sheet pan. Brush or spray the dough pieces with a little oil, cover with plastic and refrigerate overnight (or for up to two days).
Step 5When ready to bake, place a pizza stone on the bottom of the oven and heat it to 500 degrees. Remove the dough from the refrigerator and, with a rolling pin on a floured surface, roll out each portion into a 5- to 6-inch circle, making sure to keep the top of the roll the same as when it was proofed. Depending on the size of your stone and oven, you can bake one at a time or more. Place the circles of dough on the hot stone and bake until the pitas puff up and are lightly colored, 3 to 4 minutes. Pull out the pitas using a spatula, tongs or a peel and cool while you bake the remainder. Don’t stack them until they’re cool.