Preheat oven to 350°F and grease a 9x13-inch baking dish with cooking spray or butter.
Steam or blanch the broccoli florets in boiling water for 3-4 minutes until bright green and slightly tender, then drain very well and pat dry.
In a large mixing bowl, combine cream of mushroom soup, sour cream, mayonnaise, milk, 2 cups of shredded cheddar cheese, garlic powder, onion powder, salt, and pepper, stirring until smooth.
Add the broccoli to the cheese mixture and fold gently until all florets are well coated, then spread evenly into the prepared baking dish.
In a small bowl, combine crushed crackers with melted butter and remaining 1/2 cup of cheese, then sprinkle evenly over the broccoli mixture.
Bake uncovered for 30-35 minutes until the casserole is bubbling around the edges and the topping is golden brown.
Let stand for 5 minutes before serving to allow the casserole to set up slightly.