Preheat oven to 400°. Place a baking sheet in oven.
Brush pizza crust with oil. Sprinkle crust with garlic. Sprinkle crust with 3 tablespoons mozzarella. Top with arugula, prosciutto, basil, asparagus, and mushrooms. Sprinkle with remaining 7 teaspoons mozzarella and Parmigiano-Reggiano. Place pizza on preheated baking sheet; bake at 400° for 20 minutes or until golden brown. Let stand 5 minutes before slicing into 4 wedges.