- 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.