Start by preheating your oven to 375°F (190°C). Grease a 9×13 inch baking dish with non-stick cooking spray or a little bit of butter to ensure the cheese doesn’t stick to the sides.
In a large mixing bowl, whisk together the condensed cream of chicken soup, sour cream, milk, garlic powder, onion powder, salt, and pepper. Once smooth, stir in 1 cup of the shredded cheddar cheese.
Add the cooked chicken and the steamed broccoli florets to the bowl with the cheese sauce. Gently fold everything together until the chicken and broccoli are thoroughly coated in the creamy mixture.
Pour the mixture into your prepared baking dish and spread it out evenly. Sprinkle the remaining 1 cup of cheddar cheese over the top. In a small bowl, mix the cracker crumbs with the melted butter and sprinkle them over the cheese layer for a crunchy finish.
Place the dish in the oven and bake for 25 to 30 minutes. You are looking for the sauce to be bubbling around the edges and the cracker topping to be a beautiful golden brown. Remove from the oven and let it sit for 5 minutes before serving.