Heat the oven to 375°F and grease a 9-by-13-inch dish. Boil rigatoni 2 minutes short of done, adding broccoli for the final 2 minutes; drain well.
Brown the beef and onion and drain. Melt butter in the skillet, add garlic for 30 seconds and flour for 1 minute.
Whisk in milk, salt and pepper and simmer until lightly thick. Stir in 1 cup Parmesan.
Fold in beef, pasta, broccoli and 1 cup mozzarella. Spread in the dish and top with remaining mozzarella and Parmesan.
Bake for 25 to 30 minutes until bubbling and browned. Rest 10 minutes.