01 - Preheat oven to 375°F. Grease a 9x13-inch baking dish.
02 - Boil pasta in salted water until just al dente, about 1–2 minutes less than package directions. Add broccoli florets during the last 2 minutes. Drain and set aside.
03 - Melt butter in a saucepan over medium heat. Add minced garlic and sauté for 30 seconds until fragrant. Stir in flour and cook for 1 minute, forming a roux.
04 - Gradually whisk in whole milk and heavy cream, stirring constantly until smooth. Simmer gently for 3–4 minutes until sauce thickens slightly.
05 - Lower heat and stir in Parmesan, mozzarella, salt, black pepper, and nutmeg. Remove from heat once cheese is fully melted and sauce is smooth.
06 - In a large bowl, toss cooked pasta, broccoli, chicken, and Alfredo sauce until evenly coated.
07 - Transfer mixture to prepared dish and evenly sprinkle with mozzarella and Parmesan cheeses.
08 - Bake for 20–25 minutes until bubbling and golden on top.
09 - Allow to rest for 5 minutes before garnishing with chopped parsley and serving.