Preheat your oven to 350°F (175°C). Lightly grease a 9x13 inch baking dish.
In a large mixing bowl, whisk together the sour cream, mayonnaise, dried minced onion, curry powder, garlic powder, salt, and black pepper until well combined and smooth.
Gently fold in the cooked chicken, steamed broccoli, and three-quarters of the shredded cheddar cheese into the sauce mixture.
Pour the entire mixture into your prepared baking dish, spreading it evenly.
Sprinkle the remaining one-quarter of shredded cheddar cheese over the top of the casserole.
Bake for about 35 minutes, or until the casserole is hot and bubbly, and the cheese on top is melted and lightly golden brown.