Position a rack in the lower third of the oven. Place a pizza stone on the rack and preheat the oven to 500°F (260°C). Preheat for 45 to 60 minutes to allow the stone to absorb as much heat as possible.
Cover a baking sheet with aluminum foil. Scatter the cherry tomatoes over. Drizzle with 1 tbsp (15 ml) olive oil, then season with salt and pepper. Set the baking sheet over the pizza stone and roast the tomatoes until their skins split and becomes blackened in spots, 10 to 12 minutes. Remove and let cool slightly. Leave the oven on.
Roll out the Roman pizza dough
Sprinkle a clean, working surface and one of the balls of pizza dough with flour. Roll out the dough in a very thin, large rectangle with rounded corners.
Cut out a piece of parchment paper large enough to hold the pizza crust. Fold the crust in half and transfer to the parchment paper (the paper will make it easier to transfer the pizza to the oven, as the thinness of the crust would make it virtually impossible to slide the pizza off onto the stone). Cover the crust with a clean kitchen towel and let rest for 15 minutes.
Garnish and bake the pizza
Generously brush the pizza crust with extra-virgin olive oil. Sprinkle with the grated Parmigiano-Reggiano, then distribute the slices of buffalo mozzarella over the crust. Nestle the roasted tomatoes in between the mozzarella slices. Season with salt and pepper.
Using a pizza peel or a large cutting board, carefully transfer the pizza (with the parchment paper) onto the preheated pizza stone in the oven. Bake until the crust is browned and crisp and the cheese is bubbly, about 10 minutes.
SERVING: Pull the pizza out of the oven. Sprinkle with the arugula and some fresh basil leaves, if desired. Serve immediately.
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