In a medium saucepan, heat 1 tablespoon of olive oil over medium heat. Add the chopped onion and sauté until translucent, about 4-5 minutes. Then, add the minced garlic and cook for another minute until fragrant.
In a separate pot, bring 2 cups of vegetable broth to a boil. Add the uncooked brown rice to the boiling broth. Reduce the heat to low, cover, and simmer for about 40-45 minutes, or until the rice is cooked and liquid is absorbed.
While the rice is cooking, bring a pot of water to a boil. Add the broccoli florets and blanch for 2-3 minutes, then drain and set aside. This will keep the broccoli vibrant and tender-crisp.
Once the rice is cooked, add the sautéed onion and garlic mixture to the rice, along with the blanched broccoli. Stir to combine.
Pour in the milk, and sprinkle in the paprika, salt, and pepper. Stir everything together to combine.
Gradually add the shredded cheddar cheese, mixing until melted and creamy. Adjust seasoning to taste, adding more salt, pepper, or crushed red pepper flakes as desired.
Serve hot directly from the skillet, garnished with additional cheese or a sprinkle of paprika if you like.
Notes
Optional: Add crushed red pepper flakes for extra heat.