Trim the stem end of the brussels sprouts and peel off the outer leaves (go about halfway down). Place leaves in a medium bowl and drizzle with olive oil (about 1 teaspoon). Using your hands, toss the leaves in the oil so they are evenly glistening. Season with a sprinkling of kosher salt. Set aside. Save the remaining sprouts for another use.
Preheat an oven to 500°F, and set an oven rack in the lowest possible position. Lightly coat a pizza pan with nonstick cooking spray.
Stretch pizza dough into a round large enough to fit the pizza pan. Very lightly drizzle the dough with olive oil, using your hands to evenly spread the oil around. Sprinkle dough with a small pinch of kosher salt. Top pizza evenly with grated mozzarella cheese, then spread the sauce evenly over the cheese. It may seem like it's not enough sauce, but trust me, it is. Season with a sprinkling of kosher salt. Drape prosciutto slices around the surface of the pizza, then scatter brussels sprout leaves over top. Finish with several grinds of black pepper and an even dusting of Parmesan cheese.
Transfer pizza to the oven on the lowest rack and cook until the crust is golden brown (bottom and crust) and the cheese is nice and bubbly (9 - 11 minutes).