Preheat oven to 350°F (175°C) and lightly grease a 2-quart baking dish.
In a large mixing bowl, whisk together the condensed cream of chicken soup, sour cream, garlic powder, onion powder, and black pepper until smooth.
Fold in the cubed chicken, blanched broccoli, and 1.5 cups of the shredded cheddar cheese.
Transfer the mixture to the prepared baking dish and spread into an even layer.
In a separate small bowl, combine the crushed crackers and melted butter until evenly coated.
Sprinkle the remaining 0.5 cup of cheddar cheese over the casserole, followed by the buttered cracker crumbs.
Bake for 25 to 30 minutes, or until the sauce is bubbling and the topping is golden brown.
Remove from oven and let stand for 5 minutes before serving.