Preheat your oven to 350°F (175°C). Grease a casserole dish and set aside.
In a large skillet, melt the butter over medium heat. Add the flour and whisk until smooth to form a roux.
Gradually pour in the milk while whisking constantly to prevent lumps from forming. Cook until the mixture thickens and begins to bubble.
Stir in the garlic powder, onion powder, salt, and pepper, to taste. Cook for an additional minute, then remove the skillet from heat.
In a mixing bowl, combine the cooked chicken, cooked rice, blanched broccoli florets, and half of the shredded cheddar cheese.
Pour the creamy sauce over the chicken, rice, and broccoli mixture, stirring until everything is evenly coated.
Transfer the mixture to the prepared casserole dish, spreading it out into an even layer.
Sprinkle the remaining shredded cheddar cheese over the top of the casserole. If desired, top with breadcrumbs or crushed crackers for added crunch.
Cover the casserole dish with foil and bake in the preheated oven for 20 minutes.
Remove the foil and bake for an additional 10 to 15 minutes, or until the cheese is melted and bubbly and the casserole is heated through.
Once done, remove the casserole from the oven and let it cool for a few minutes before serving.