Preheat your oven to 350°F (175°C). Grease a baking dish.
In a large bowl, combine the cooked chicken and blanched broccoli.
In another bowl, mix together the mayonnaise, cheddar cheese, sour cream, Parmesan cheese, Dijon mustard, garlic powder, salt, and pepper until well combined.
Pour the cheesy sauce over the chicken and broccoli. Stir to evenly coat all ingredients.
Transfer the mixture into the greased baking dish, spreading it out evenly.
In a small bowl, combine the crushed buttery crackers and melted butter. Sprinkle this mixture evenly over the casserole.
Place the baking dish in the preheated oven and bake for about 25-30 minutes or until the casserole is bubbling and the topping is golden brown.