01 - Preheat oven to 375°F. Lightly grease a 9x13-inch baking dish and set aside.
02 - Bring a large pot of salted water to a boil. Add pasta and cook until al dente, about 1-2 minutes less than directed on the package. Drain well and set aside.
03 - Steam or blanch chopped broccoli florets for 2-3 minutes until bright green and just tender. Drain and set aside.
04 - In a large saucepan over medium heat, melt butter. Add the minced garlic and sauté for 1 minute until fragrant. Pour in heavy cream, bring to a gentle simmer, then whisk in 1 cup Parmesan cheese until sauce thickens and becomes smooth. Season with salt, black pepper, and ground nutmeg if using.
05 - In a large mixing bowl, combine cooked pasta, diced or shredded chicken, steamed broccoli, and Alfredo sauce. Toss until thoroughly coated.
06 - Spread the combined mixture evenly into the prepared baking dish. Sprinkle shredded mozzarella and 1/4 cup Parmesan cheese evenly over the top.
07 - Bake in the preheated oven for 20-25 minutes, or until the top is golden and the casserole is bubbling.
08 - Remove from oven and let stand for 5 minutes before serving. Garnish with fresh parsley if desired.