Preheat the oven to 350°F (175°C).
Cook the egg noodles according to package instructions until al dente. Drain and set aside.
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, milk, garlic powder, onion powder, salt, and black pepper. Stir until smooth.
Add the cooked chicken, steamed broccoli, cooked noodles, and shredded cheddar cheese to the bowl. Mix everything together until well combined.
Lightly grease a 9×13 inch baking dish with butter or cooking spray.
Pour the mixture into the prepared baking dish and spread evenly.
Melt the 2 tablespoons of unsalted butter in a small bowl and mix with the crushed buttery crackers.
Sprinkle the cracker mixture evenly over the casserole.
Bake in the preheated oven for 30 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.