Add 2 tablespoons of vegetable oil to each of two 6- or 7-inch round cake pans, swirling to coat the bottom and about 1 inch up the sides.
Divide the dough in half. Press one piece into each oiled pan with your fingertips, working it toward the edges. It will not reach the sides yet. Do not use a rolling pin.
Cover loosely and let rise in a warm spot for 60 to 90 minutes, until the dough has puffed and spread to fill the pan.
Preheat the air fryer to 350 degrees F.
Spread 1/4 cup of pizza sauce over each risen dough, leaving a thin border. Sprinkle with Parmesan and oregano.
Add the mozzarella, pushing it all the way to the edge of the pan so it touches the metal. Add the pepperoni, tucking a few slices under the cheese.
Place one pan in the air fryer basket and cook for 12 to 16 minutes, until the cheese is melted and spotted golden and the crust edge is deep golden brown. Repeat with the second pan.
Immediately slide a spatula under the pizza and lift it out of the pan onto a wire rack or cutting board. Rest 3 to 5 minutes, then slice and serve.