01 - Preheat oven to 375°F. Thoroughly grease a 9x13-inch baking dish.
02 - In a large pot of salted boiling water, cook the penne or rigatoni pasta until al dente. During the final 2 minutes of pasta cooking, add the broccoli florets to the pot. Drain the pasta and broccoli well, then set aside.
03 - In a large skillet over medium heat, melt the unsalted butter. Add the minced garlic and sauté for 1 minute until it becomes fragrant.
04 - Pour the heavy cream into the skillet and bring it to a gentle simmer. Stir in 1 cup of Parmesan cheese and 1/2 cup of mozzarella cheese, continuously stirring until the cheeses are melted and the sauce is smooth. Season the sauce with salt, black pepper, and ground nutmeg, if using.
05 - In a spacious mixing bowl, combine the cooked pasta, broccoli, diced chicken, and the prepared Alfredo sauce. Mix all ingredients thoroughly to ensure everything is evenly coated.
06 - Transfer the pasta mixture into the prepared 9x13-inch baking dish. Evenly sprinkle the remaining 1/2 cup of mozzarella cheese and 1/2 cup of Parmesan cheese over the top.
07 - Bake the casserole uncovered for 20 minutes, or until the sauce is bubbly and the cheese topping is golden brown.
08 - Allow the chicken alfredo bake to rest for 5 minutes before garnishing with fresh parsley, if desired, and serving.