In the bottom third of your oven, place a pizza stone or a rimmed baking sheet.
Preheat the oven to 550 degrees F or as high as possible (at least 475 degrees F).
Let the pizza stone heat for at least 30 minutes.
Using the extra oil, lightly grease a work surface. Using flour is not recommended as it can make the dough tough.
Place the pizza dough in the center of the prepared work surface and, using your hands, press it down starting from the center.
Keep gently patting and stretching the dough out, moving outward from the center until you have a circle about 12 inches across.
Transfer the dough to a square of parchment paper.
Drizzle 1 tablespoon of the remaining olive oil on the top of the dough and, using your hands or a pastry brush, rub the oil all over the top of the dough. Make sure to especially rub the border with the oil.
Optionally, let the dough rest for 10 minutes. This will help ensure a thicker crust.
Pull the edges of the parchment paper to slide the pizza dough circle onto a pizza peel or a flat baking sheet.
Using the peel, carefully slide the pizza dough and the parchment paper onto the pizza stone while it is still in the oven.
Bake the pizza dough until it is slightly puffed, about 1-2 minutes.
Use the parchment paper to pull the pizza dough onto the peel and immediately transfer the dough from the oven, shutting the oven door as quickly as possible.
Poke down any large bubbles in the dough.
With the dough circle still on the peel, add the pizza sauce to the center of the dough circle and spread it out evenly across the pizza, leaving only the edges.
Top the pizza sauce with the mozzarella slices and then sprinkle with the shredded mozzarella.
Evenly distribute the pepperoni slices across the cheese layer on the pizza.
Sprinkle 2 tablespoons of the parmesan over the cheese-pepperoni layers.
Using the same technique as when you par-cooked the dough, transfer the pizza to the pizza stone or pan in the oven, but without the parchment paper this time.
Bake the pizza until the cheese is melted bubbly, and starting to lightly brown, the edges of the crust are golden-brown, and the crust is cooked through, about 8-12 minutes.
Using the peel, transfer the pizza to a wire rack to cool slightly.
Slice and serve the pizza garnished with the extra parmesan and the parsley.