01 - Preheat oven to 375°F. Grease a 9x13-inch baking dish with butter or cooking spray.
02 - Bring a large pot of salted water to boil. Cook pasta until just al dente, about 2 minutes less than package directions. Add broccoli florets during the final 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 - Gradually add grated Parmesan and shredded mozzarella, stirring continuously until melted and sauce is smooth and slightly thickened, about 3-4 minutes. Season with salt, black pepper, and ground nutmeg.
06 - In a large mixing bowl, combine cooked chicken, drained pasta and broccoli mixture, and Alfredo sauce. Toss until all ingredients are evenly coated.
07 - Transfer mixture to the prepared baking dish, spreading evenly. Sprinkle topping cheeses over the surface in an even layer.
08 - Bake for 20-25 minutes until bubbly and golden brown on top. The cheese should be melted and slightly browned.
09 - Let casserole rest for 5 minutes before serving to allow sauce to set slightly. Garnish with fresh chopped parsley if desired.