Preheat oven to 450°F.
To start the dough, mix together the yeast, warm water, and honey in a small bowl. Let it sit for about 10 minutes to proof. You’ll see bubbles form on top.
Combine the different flours and salt in a large bowl. In the middle of the bowl, create a well in the middle. That’s where you’ll add the yeast mixture.
Combine the wet and dry ingredients, mixing with your hands. Knead the dough for 5 minutes, adding more flour if needed. The dough should be soft, not flaky or sticky.
Lightly coat a bowl with the oil and place the dough ball inside. Cover with plastic wrap, or a towel, and let it rest in a warm place for about 30 minutes.
Divide the dough into 6 portions. Shape it into a ball. Place the balls onto a clean, floured surface. Roll out each ball with a rolling pin into a ¼-inch thick circle. Transfer to a parchment-lined cookie sheet.
Bake each pita for 5 minutes or until the pita puffs up.
Eat warm, use it as a wrap for Gyros, or store in an airtight container for later.