Position an oven rack on the second highest position, put a pizza stone on it and preheat the oven for 1 hour to as high as your oven goes, usually 500 to 550 degrees F.
Divide the pizza dough into 2 pieces. On a floured surface, gently roll out each piece of dough into a 10- to 12-inch circle. Transfer one piece of dough to a floured pizza peel or the back of a baking sheet. Ladle about 1/4 cup of the Alfredo sauce on the pizza, leaving a 1/4-inch border. Top with half the mozzarella. Transfer to the pizza stone and bake until golden and bubbly, rotating halfway through, about 10 minutes. Remove from the oven and top with half the prosciutto slices. Next, scatter with half of the figs. Bake for another 2 to 3 minutes. Repeat with the remaining dough and pizza toppings.
Meanwhile, whisk together the balsamic, olive oil and crushed red pepper with some salt and pepper in a medium bowl. Toss with the arugula.
Top the warm pizzas with the dressed arugula, slice and serve immediately.