Brown beef and onion in a deep 12-inch saute pan over medium-high heat for 8 minutes, breaking up the meat and cooking to 160°F. Drain excess fat.
Stir in garlic for 30 seconds, then drained rice for 1 minute. Add broth, salt and pepper and bring to a boil.
Cover tightly, lower heat to low and cook for 15 minutes without lifting the lid.
Quickly scatter broccoli over the rice, cover again and cook for 5 to 7 minutes until rice is tender and broccoli can be pierced easily. If rice is still firm and the pan looks dry, drizzle in reserved water and cover for another 3 minutes.
Remove from heat and rest covered for 5 minutes. Fold in cheddar gently, cover for 1 minute to melt it and serve.