Preheat a grill to medium-high heat.
Place the pizza dough on the grill. Let cook for 1 minute, and then flip with tongs. Move to a cooler spot on the grill (about medium heat) until the dough begins to pull away from the grill, about 1 minute. Remove the dough from the grill.
Spread the dough with the ricotta and scatter with mozzarella. Return to the grill, cover and cook until the cheese melts, about 3 minutes. Top with the prosciutto and arugula and drizzle with olive oil.