Let's make pita! Place the yeast, sugar and warm water in the bowl of a stand mixer with hook attachment. Or you can do this by hand in a large bowl. Let sit for 10 minutes until foamy (if it doesn't form, your yeast is dead or the water was the wrong temperature and you killed it. Sad.)
Add the oil and gradually add 2 cups whole wheat flour with the mixer on low speed. Then add the salt and turn the speed up to medium-high and mix for 6-8 minutes. Keep adding bread flour until dough is smooth and elastic and slightly sticky. Do not add too much flour. You can also knead by hand. I did!
Clean out the bowl and place dough in the clean bowl coated with oil, cover with a towel or plastic wrap, and let rise in a warm spot for 2 hours, or until doubled in size.
When the dough is ready, divide the dough into 6 equal-sized balls (or more or less depending on how big you want your pitas) and fatten into ½ inch thick discs. Place pitas on parchment paper, cover lightly, and let rise 30 more minutes.
Preheat oven to 500 degrees F. Place a baking sheet in the oven to pre-heat as well.
At this point you can bake the pita for puffier pitas, or roll out for pitas with a pocket.
Roll each pita out to 1/4 inch thick. Don't roll more than you need as this will affect the pocket making process! Cover and let rest for 10 more minutes.
Carefully flip the pitas over, spritz with a little water to help with steaming (optional) and carefully place on the hot baking sheet at least 1-inch apart. You will need to bake in batches. Bake for 5-6 minutes, until puffy and slightly brown. Do not overcook. Remove from the oven, brush with olive oil and sprinkle with za'atar. Eat! Keeps in an airtight container for up to three days; reheat before serving.
Note- you will also need 2 1/2 hours proofing time.