Preheat your oven to 350°F (175°C).
In a large pot, bring water to a boil. Add the broccoli florets and cook for 3-4 minutes until tender but still crisp. Drain and set aside.
In a saucepan over medium heat, melt the butter. Once melted, whisk in the flour to create a roux and cook for about 2 minutes until bubbly.
Gradually add the milk while whisking continuously until smooth. Cook until the mixture thickens, about 3-5 minutes.
Remove the saucepan from the heat and stir in 1 ½ cups of cheddar cheese, garlic powder, onion powder, salt, and black pepper until fully combined and melted.
In a mixing bowl, combine the cooked rice, broccoli, and cheese sauce. Stir until well coated.
Pour the broccoli and cheese mixture into a greased 9x13-inch baking dish. Spread it evenly.
Top with remaining cheese and breadcrumbs, distributing evenly over the casserole.
Bake in the preheated oven for 25-30 minutes or until the top is golden brown and bubbling.
Let cool for a few minutes before serving.