Preheat to 375°F (190°C) and grease a 9x13-inch baking dish.
Boil salted water, cook pasta until al dente, drain, and set aside.
Steam florets for 3–4 minutes or microwave with 1 tbsp water for 2–3 minutes. Drain well.
Melt butter in a saucepan over medium heat. Whisk in flour for 1 minute until smooth.
Slowly whisk in milk and cream. Simmer 4–5 minutes, stirring, until thickened.
Lower heat, stir in Parmesan, garlic powder, onion powder, salt, and pepper. Stir until smooth.
Mix pasta, chicken, and broccoli in a large bowl. Add sauce and fold to coat.
Pour into the dish, spread evenly, and top with mozzarella.
Bake 20–25 minutes until bubbly and golden. Broil 1–2 minutes for extra browning, if desired.
Let rest 5 minutes. Garnish with parsley, red pepper flakes, or extra Parmesan.