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In a large, oven-safe bowl, whisk together the flours with the salt, yeast, and malt powder, if using.
Stir in the water, followed by the olive oil.
Continue to stir until the dough comes together. Knead a few times with your hand to form the dough into a ball.
Cover the bowl with plastic wrap. Transfer to the oven and proof until doubled in size, about 1 ½ hours. Remove from the oven.
Place a cast iron skillet or pizza stone on a rack in the middle position before adjusting the oven. Let the skillet heat up with the oven.
On a floured counter, divide the dough into four even pieces.
Roll each round briefly in the flour on the counter. Transfer to a square of parchment paper. Cover with plastic wrap. Let rise at room temperature for 35 minutes.
Roll each pita into a 6- to 7-inch circle. You can start by using your hands to press it into shape, then use a rolling pin to form the circle. Add flour as needed to prevent sticking.
Working with one pita at a time, carefully place onto the hot cast iron skillet and bake until puffed and lightly golden, about 6 minutes. Transfer to a plate.
Repeat the baking process with the remaining pita rounds.
Serve immediately or save and toast before serving.