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 instructions; add broccoli for the last 2 minutes. Drain and set aside.
03 - Melt butter in a saucepan over medium heat. Add garlic and sauté for 30 seconds.
04 - Whisk in flour and cook for 1 minute. Gradually add milk and cream, stirring constantly until smooth. Simmer gently until slightly thickened, about 3–4 minutes.
05 - Reduce heat to low. Stir in Parmesan, mozzarella, salt, pepper, and nutmeg until cheese melts and sauce is smooth. Remove from heat.
06 - In a large bowl, combine cooked pasta, broccoli, chicken, and sauce, mixing thoroughly for even coating.
07 - Transfer mixture to prepared baking dish. Sprinkle with mozzarella and Parmesan cheese.
08 - Bake for 20–25 minutes until bubbly and golden on top.
09 - Allow to rest for 5 minutes before garnishing with parsley and serving.