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Step 1
Add yeast to a bowl and add half cup of lukewarm water and sugar. Whisk until yeast is dissolved. If the yeast doesn't bubble up slightly on the surface then your yeast is likely dead. Start again with fresh yeast.
Step 2
Place all purpose flour and whole wheat flour the bowl of a stand mixe and pour in the yeast mixture. Start the mixer on the lowest setting and add more water, little bit at a time and knead until there are no dried bits of flour. Add the olive oil at this stage as well.
Step 3
Once the dough has come together, stop the mixer, add the salt and knead again for 1-2 minutes. Remove the dough from the stand mixer and knead by hand, stretching and folding the dough onto itself for 2-3 minutes.
Step 4
Form the dough into a smooth ball, rub with a few drops of olive oil all over the dough and transfer to a bowl or leave it on your work surface. Cover with a damp kitchen towel and leave for an hour to rise.
Step 5
Preheat the oven to 500 degrees F. Preferably, use a pizza stone or steel and heat that on the middle rack as the oven preheats.
Step 6
Once the dough has roughly doubled in size, cut the dough into 8 equal balls for small pitas or 4 equal parts for large pitas. You can go anywhere in between as well. Shape the portions into a ball and dust your work surface with flour. Lightly dust the balls with flour and pat them down slightly. Cover with a damp kitchen towel and allow to rest for 5-10 minutes.
Step 7
Take each portion and flatten with a rolling pin to roughly 1/8 to 1/4 inch of thickness. Cover all the portions again with a kitchen towel. Allow to rest for 5-10 minutes.
Step 8
To cook in the oven: Place the flattened portions on the hot pizza stone/steel - you can use a pizza peel or a wooden board to help transfer the dough. Or, if you are not using a pizza stone/steel, use the back of a baking sheet (make sure to heat that for 5 minutes or so before transferring the dough.
Step 9
Bake/cook until the pita puffs up completely and avoid opening the oven while this happens. You may have to work in multiple batches to cook all the dough portions. Once out of the oven, let the pitas cool down before storing.
Step 10
To cook on the stovetop: Heat a cast iron pan on medium to medium high heat until its lightly smoking and then place the rolled out dough on the pan.
Step 11
The bread will start to slowly puff up, monitor the underside of the bread and once that side is lightly browned, flip and do the same on the other side.
Step 12
Then, on another stovetop, place a wire rack and turn the heat to high. Place the browned bread directly on the wire rack and allow the direct heat from the stove to finish puffing and cooking the bread.