Preheat the oven to 550 degrees F, or to as high as your oven will go.
Drizzle 1 to 2 tablespoons oil over a 13-x-18-inch sheet pan. Place one ball of on the sheet pan and gently stretch out towards the edges; it should stretch to within 1 inch of the edge of the pan all the way around. If the dough resists stretching and springs back, set it aside for a few minutes to relax, then try again. Repeat this with the other ball of dough on a second sheet pan.
For the pesto, pea and burrata pizza: Combine the peas and salt in a small bowl and mash with a fork. Set aside.
Drizzle one stretched pizza crust with 1 to 2 tablespoons oil, then bake it until the edges start to turn golden and the middle puffs up slightly, about 7 minutes. Remove the crust from the oven and top with the pesto, peas and another drizzle of oil. Bake until browned around the edges and bubbling, about 5 minutes longer.
Remove the pizza from the oven. Tear the burrata into chunks and dot it over the pizza. Sprinkle with the Parmesan, basil and black pepper. Slice and serve.
For the Margherita with prosciutto pizza: Stir the tomato paste, oil, salt and pepper together in a small bowl. Spread the mixture over the other stretched pizza dough in a thin even layer. Sprinkle with the mozzarella.
Place in the oven and bake until puffed and golden around the edges, 8 to 10 minutes. Remove from the oven and top with the prosciutto, basil leaves and arugula. Drizzle with a little more oil and sprinkle with pepper and flaked salt. Slice and serve.