01 - Preheat oven to 375°F. Lightly grease a 9x13-inch baking dish.
02 - Boil pasta in salted water for 2 minutes less than package instructions. Add broccoli florets for the last 2 minutes of boiling. Drain and set aside.
03 - In a large skillet over medium heat, melt butter. Add minced garlic and cook for 30 seconds until fragrant. Add shrimp and sauté for 2 to 3 minutes until just pink. Using a slotted spoon, remove shrimp and set aside.
04 - To the same skillet, pour in heavy cream and bring to a gentle simmer. Stir in Parmesan and mozzarella cheese, salt, black pepper, and nutmeg. Simmer, stirring, until the cheese is melted and sauce is creamy, about 2 to 3 minutes.
05 - Add cooked pasta, broccoli, and sautéed shrimp to the sauce. Toss thoroughly to ensure all ingredients are evenly coated.
06 - Transfer the mixture evenly into the prepared baking dish. Sprinkle with the remaining mozzarella and Parmesan cheese.
07 - Bake for 20 to 25 minutes until the bake is bubbling and the top is golden brown.
08 - Sprinkle with chopped parsley if desired. Serve immediately while hot.