Dough. In a large bowl, us a whisk or spoon to combine together the all purpose flour, whole wheat flour, instant yeast, salt, and sugar. Then make a well in the center of the mixture and add the warm water and olive oil. Continue to mix the ingredients until the dough becomes sticky to touch. Then allow the dough to rest for five to 10 minutes for the water to to absorb and the gluten to relax.
Knead While the dough is sitting you can prepare a clean workspace that is lightly dusted with flour to use for kneading. You will also need a clean bowl that is well greased. Turn the dough out onto your floured surface and knead for five to seven minutes until the dough is smooth and soft. The dough should be very wet so avoid adding too much extra flour. I like to use a stretch and fold style of kneading rather than trying to work the dough with your whole hand. Alternatively, you can use a stand mixer with a dough hook for this step.
Rise. Transfer the dough to your prepared greased bowl, cover with a damp cloth or plastic wrap, and allow the dough to rise until 2.5-3x the size, about 1 hour depending on temperature in your room.
Prepare. Preheat your oven to 450°F/230 C. Place a heavy baking sheet in the oven to heat while the oven preheats. Meanwhile, place the dough on a clean lightly floured workspace and divide the dough into eight pieces. With each piece, roll the dough between your palms to form a ball. Set aside to rest for five to seven minutes covered with a cloth so the gluten relaxes.
Roll Out On a clean and well-floured surface, use a rolling pin to roll out each piece into an 8”/20cm circle slightly more than ¼”/6mm thick. Then rest the formed pitas for 10 minutes.
Bake Carefully place the pita bread on to the warmed baking sheet about two inches apart from one another so that they will have enough room to to puff properly. You will most likely have to bake two to three pitas at a time. Bake the pita rounds for two to four minutes or until they are puffed and lightly golden in color. Remove the baked pitas immediately and place a new batch into the oven. Once removed from the oven the pitas will collapse, but will still have the pocket inside when cut open. You can cover the baked pita bread with a clean kitchen towel to keep them soft.