Preheat an oven to 475 degrees F (245 degrees C). Line baking sheets with aluminum foil.
Sprinkle pancetta into a cold skillet and drizzle 1 teaspoon olive oil over pancetta. Cook and stir pancetta over medium heat until browned and caramelized, 5 to 10 minutes. Remove pan from heat and cool pancetta in the oil in the skillet.
Place 1 dough quarter on a work surface and lightly dust with flour; roll into a 1/8-inch-thick irregularly shaped crust. Stretch dough with your hands to an even thickness; let rest on the work surface for 5 minutes. Repeat with remaining dough.
Heat about 1 cup olive oil, reaching about 1/2-inch depth, in a heavy cast iron skillet over medium-high heat. Fry each piece of dough until browned and cooked through, about 2 minutes per side. The first side will be lighter than the second side. Drain the crusts on paper towels.
Transfer pizza crusts, lighter-side up, to prepared baking sheets. Spread about 2 tablespoons ricotta cheese onto each crust using the back of a spoon. Sprinkle about 1/2 teaspoon fresh thyme over ricotta layer. Sprinkle pancetta over the ricotta-thyme layer; season with black pepper. Nestle about 5 peach slices onto each pizza, working around the pancetta pieces. Sprinkle 1 tablespoon Parmesan-Reggiano cheese over each pizza. Drizzle about 1 teaspoon extra-virgin olive oil over Parmesan-Reggiano layer.
Bake in the preheated oven until cheese is melted and peaches are lightly browned and tender, 12 to 15 minutes. Cool pizzas for 5 to 10 minutes on the baking sheet.
