01 - Preheat oven to 375°F. Grease a 9x13-inch baking dish with cooking spray or butter.
02 - Cook pasta in salted boiling water until just al dente, about 2 minutes less than package instructions. Add broccoli florets during the last 2 minutes of cooking. Drain well and set aside.
03 - In a large saucepan over medium heat, melt butter. Add minced garlic and sauté for 1 minute until fragrant, being careful not to brown.
04 - Pour in heavy cream and whole milk. Bring to a gentle simmer over medium heat, stirring frequently to prevent scorching.
05 - Add Parmesan and mozzarella cheese, stirring until completely melted and sauce is smooth and slightly thickened, about 3-4 minutes. Season with salt, black pepper, and nutmeg.
06 - In a large mixing bowl, combine cooked chicken, drained pasta and broccoli, and prepared Alfredo sauce. Mix until all ingredients are evenly coated.
07 - Transfer mixture to the prepared baking dish, spreading evenly. Sprinkle topping cheeses uniformly across the surface.
08 - Bake for 20-25 minutes, or until sauce is bubbly around edges and cheese topping is golden brown.
09 - Let casserole rest for 5 minutes before serving to allow sauce to set. Garnish with chopped fresh parsley if desired.