Position an oven rack to the upper-middle position, place a baking stone on the rack, and heat the oven to 500°F. Allow the stone to heat for at least 30 minutes before baking to ensure the bottom of the crust crisps immediately on contact.

Divide the pizza dough into two equal pieces. On a lightly floured surface, roll or stretch each piece into a 14-inch circle, maintaining a slightly thicker border at the edges.

Transfer each dough round to a piece of parchment paper. Brush the outer edges of the dough with olive oil to encourage browning, then spread the pizza sauce over the center, leaving a 1-inch border.

Sprinkle the mozzarella cheese and Parmesan cheese evenly over the sauce on both pizzas.

Slide the first pizza, while still on the parchment, onto the hot baking stone. Bake until the crust is deeply browned and the cheese is melted and beginning to brown in spots, 8 to 12 minutes.

Transfer the pizza to a wire rack and let it rest for 5 minutes so the cheese sets before slicing. Repeat the baking process with the second pizza and serve warm.