Prepare the pasta according to the package directions. Add the broccoli during the last 4 minutes of the cooking time. Drain the pasta and broccoli well in a colander.
Sir the soup, milk and black pepper in a 12x8x2-inch shallow baking dish. Stir in the pasta mixture, 3/4 cup of mozzarella cheese and 2 tablespoons of the Parmesan cheese. Top with the remaining mozzarella and Parmesan cheeses.
Bake at 350 degrees for 25 minutes or until hot and the cheese melts.