Invert a large baking sheet and place it on a rack in the lower third of the oven; preheat the oven to 500 degrees . Invert a second baking sheet on a work surface and cover it with a sheet of parchment paper. Stretch the pizza dough to fit the parchment paper. Using the back of a spoon, spread the pesto over the dough.
Slide the pizza and the parchment from the cool baking sheet to the hot baking sheet in the oven. Bake until golden, about 7 minutes. Top with the prosciutto, arugula and parmesan, and cut into pieces.