Preheat your oven to 375°F (190°C). Lightly grease a 9×13 inch baking dish with cooking spray or a small amount of butter to prevent sticking.
In a large mixing bowl, whisk together the condensed cream of chicken soup, sour cream, garlic powder, onion powder, and black pepper until the mixture is smooth and well combined.
Gently stir in the cooked chicken, steamed broccoli florets, and 1 cup of the shredded cheddar cheese. Mix until everything is evenly coated in the creamy sauce.
Spread the mixture evenly into your prepared baking dish. Sprinkle the remaining 1 cup of cheddar cheese over the top in an even layer.
In a small bowl, toss the crushed crackers with the melted butter. Sprinkle this buttery mixture over the cheese layer to create a satisfying crunch.
Place the dish in the oven and bake for 25 to 30 minutes, or until the sauce is bubbly and the cracker topping is golden brown. Let it sit for 5 minutes before serving to allow the sauce to set.