Into a large skillet over medium-high heat, add the olive oil, When oil is hot, add the onion. Cook for 2 minutes, stirring frequently, until onion is tender. Add garlic and continue cooking for an additional 30 seconds.
Add the rice and black pepper. Stir to coat the rice with oil. Cook for 1 minute, stirring frequently, until rice is just lightly toasted.
Pour in the chicken-style broth and water. Bring to a boil then cover and reduce heat to low. Simmer, without stirring, for 12 minutes.
Gently stir in the broccoli. Replace the cover and continue cooking for an additional 6 minutes, until the rice and broccoli are tender.
Stir in the cheese. Continue cooking for an additional 2 minutes, just until the cheese is melted then serve hot.