Set a large skillet over medium-high heat and add the olive oil. When the oil is hot, add the onion. Cook for about 2 minutes, stirring occasionally, until the onion softens. Add the garlic and cook for an additional 30 seconds until fragrant.

Stir in the rice and black pepper, coating it with the oil. Continue cooking for about 1 minute, stirring frequently, until the rice is lightly toasted.

Pour in the chicken-style broth and water. Bring to a boil, then cover and reduce the heat to low. Simmer for 12 minutes without stirring.

Gently stir in the broccoli, cover, and cook for another 6 minutes, until the rice is tender and the broccoli is bright green and cooked through.

Stir in the cheddar cheese and continue cooking for 2 more minutes, or until the cheese has fully melted. Serve hot.