Heat oven to 425 degrees F. Roll and stretch dough into a large rimmed baking sheet, at least 15 x 10 x 1 inches. Sprinkle with Parmesan cheese and bake at 425 degrees F for 14 minutes or until lightly browned. Remove from oven and set aside. Reduce oven temperature to 325 degrees F.
While dough is baking, toss together tomatoes, shallot, garlic, vinegar, salt and pepper in a medium-size bowl. Spread tomatoes in an even layer in a rimmed baking sheet and roast at 325 degrees F for 30 minutes. Remove from oven and gently stir in arugula.
Sprinkle 1 cup of the mozzarella over dough and scatter tomato mixture over top using a slotted spoon. Distribute prosciutto slices over tomatoes. Sprinkle remaining mozzarella over top and bake at 325 degrees F for 15 minutes. Cool on wire rack 5 minutes, then sprinkle with basil.