Cook pasta according to package directions until al dente. Drain and set aside.
Steam or blanch broccoli florets for 3–4 minutes until tender. Drain and set aside.
In a saucepan, heat olive oil over medium heat. Stir in flour and cook for 1–2 minutes to form a roux.
Gradually whisk in heavy cream and chicken broth. Cook for 3–4 minutes until thickened.
Add garlic powder, onion powder, salt, and pepper. Taste and adjust seasoning.
In a large bowl, combine cooked pasta, shredded chicken, broccoli, and sauce. Mix well.
Transfer mixture into a greased 9×13-inch baking dish. Spread evenly.
Sprinkle cheddar and mozzarella cheese evenly over the top.
If desired, add breadcrumbs and Parmesan for a crunchy topping.
Bake at 375°F (190°C) for 25–30 minutes, until bubbly and golden.
Let casserole cool slightly before serving. Slice into portions and enjoy warm.