Divide the dough into two equal halves and shape each into a smooth, tight ball. Place them on a lightly oiled baking sheet spaced at least 3 inches apart, cover loosely with greased plastic wrap, and let stand for 1 hour. Set a baking stone on a rack 4.5 inches from the broiler element and heat the oven to 500°F for at least 30 minutes.

Heat the oil in a small skillet over medium-low heat until shimmering. Stir in the garlic, pepper, oregano, pepper flakes, and salt; cook constantly until fragrant, about 30 seconds. Transfer the mixture to a bowl to cool.

Switch the oven to the broiler for 10 minutes. Coat one dough ball generously with flour and place on a floured counter. Use your fingertips to flatten it into an 8-inch disk, leaving the outer edge slightly thicker, then gently stretch the dough into a 13-inch round and transfer to a floured pizza peel.

Spread half of the infused garlic oil evenly over the dough, leaving a quarter-inch border. Layer half of the basil leaves, half of the Pecorino, and half of the mozzarella over the oil.

Slide the pizza onto the stone and return the oven to 500°F. Bake until the crust is well browned and the cheese is bubbly, 8 to 10 minutes, rotating the pizza halfway through.

Transfer the pizza to a wire rack and dollop half of the ricotta evenly over the top. Let it rest for 5 minutes to set before slicing. Reheat the broiler for 10 minutes and repeat the process for the second pizza.