Preheat the oven to 350°F (175°C).
Steam the broccoli florets until tender but still crisp, about 4-5 minutes. Drain and set aside.
In a large mixing bowl, combine the condensed cream of mushroom soup, sour cream, mayonnaise, garlic powder, onion powder, salt, and black pepper. Stir until smooth.
Add the cooked chicken, steamed broccoli, and 1 cup of shredded cheddar cheese to the soup mixture. Stir gently to combine evenly.
Transfer the mixture to a greased 9×13-inch baking dish and spread it out evenly.
In a small bowl, mix the breadcrumbs with the melted butter until the crumbs are evenly coated.
Sprinkle the remaining 1/2 cup shredded cheddar cheese and the grated Parmesan cheese evenly over the casserole.
Top the casserole with the buttered breadcrumbs.
Bake uncovered in the preheated oven for 30-35 minutes, or until the casserole is bubbly and the topping is golden brown.
Remove from the oven and let it rest for 5 minutes before serving.