Whisk together all dry ingredients in a large mixing bowl. Add water and oil. Knead by hand. The dough should not be sticky or runny at this point. Preheat oven to 200 °F and turn off the oven. Cover the mixing bowl with lid or plastic wrap and place it in the warm oven. Let the dough rise for at least 45 minutes.
Remove the dough from the oven. Lightly dust a working surface with some gluten-free flour and transfer the pita bread dough onto the surface. Roll the dough gently to form a smooth ball and then divide the dough into 5 pieces.
Roll each piece gently to form a smooth ball and then flatten the ball to form a disc. Use a rolling pin to form each piece into a disc 5 inches in diameter. Let them rest on the counter for 5 minutes.
Preheat the oven to 375 °F. Heat a lightly greased cast iron skillet over high heat. When the skillet is hot, carefully place one disc into the skillet and reduce the heat to medium high. Cover with lid and cook for 1½ minute on each side. Transfer slightly cooked pita bread onto a large metal baking pan. Place the baking pan into the oven and bake for 3 minutes. Repeat this process for the rest of the discs.
Remove the pita breads from oven. Let them cool slightly before serving.
You may use store-bought gluten-free flour for this recipe.