Preheat oven to 375°F (190°C).
Lightly grease a 9×13-inch baking dish.
Steam broccoli for 3–4 minutes until slightly tender.
Spread broccoli evenly in the baking dish.
Top with the cooked chicken.
In a bowl, mix cream of chicken soup, sour cream, mayonnaise, garlic powder, onion powder, salt, and pepper.
Stir in 1½ cups cheddar cheese.
Spread the mixture evenly over the chicken and broccoli.
Sprinkle the remaining cheddar cheese and Parmesan cheese on top.
Mix crushed crackers with melted butter.
Sprinkle the buttery cracker mixture over the casserole.
Bake for 30–35 minutes until hot and bubbly.
Broil for 2–3 minutes for a crisp golden topping if desired.
Let rest for 5 minutes before serving.