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Combine the flour, cornstarch, sugar, baking powder, and salt in a bowl of stand mixer. In a liquid measuring cup, combine the water and oil. Turn the mixer on low speed and pour into the flour mixture. Mix until combined. Increase the speed to medium and knead until the dough forms a ball. Place the dough onto a lightly floured surface and divide the dough in half. Form a ball with each and wrap in plastic wrap. Refrigerate for at least a half hour. (Dough can be made in advance and refrigerated for up to two days.)
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On a lightly floured surface, form the dough into two 12 inch pizzas. Apply sauce and top with cheese and pepperoni.
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Preheat the oven to 475 degrees with a pizza stone on the middle rack. Allow pizza stone to heat up an additional 10 minutes after the stove reaches temperature.
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Place pizza on the stone and cook until done, about 10 - 12 minutes.
