01 - In a substantial skillet, melt the butter over medium heat. Introduce the chopped onion and sauté for 2 to 3 minutes until softened.
02 - Incorporate the minced garlic and cook for 30 seconds until aromatic.
03 - Add the uncooked rice to the skillet and stir for 1 minute to achieve a light toast.
04 - Pour in the vegetable broth and bring to a rolling boil. Reduce the heat to low, cover the skillet, and simmer for 12 minutes.
05 - Stir in the broccoli florets. Cover the skillet again and cook for an additional 7 to 8 minutes, or until the rice is tender and the broccoli is bright green and just cooked through.
06 - Remove the lid. Introduce the milk, salt, black pepper, and paprika. Increase the heat to medium-low and cook for 2 to 3 minutes, stirring constantly, until the sauce has slightly thickened.
07 - Remove the skillet from the heat. Add the shredded cheddar cheese and stir until it is fully melted and the sauce is creamy.
08 - Taste the dish and adjust seasonings as needed. Serve immediately.