In a large skillet, melt the butter over medium heat. Add the broccoli florets and sauté for about 3-4 minutes until they are tender but still bright green.
Pour in the vegetable broth and bring to a simmer. Add the cooked rice, garlic powder, onion powder, salt, and pepper. Stir to combine.
Reduce the heat to low and let the mixture simmer for about 5 minutes, allowing the flavors to meld.
Stir in the milk and half of the shredded cheddar cheese. Mix until the cheese is melted and the rice is creamy.
Remove from heat and sprinkle the remaining cheddar cheese on top. Cover the skillet for a few minutes to allow the cheese to melt.
Serve warm, garnished with additional broccoli or cheese if desired.