Rinse the rice under cold water until the water runs clear.
In a medium saucepan, bring the broth to a boil.
Add the rinsed rice to the boiling broth.
Reduce the heat to low, cover, and simmer for 15 minutes.
Remove the saucepan from heat and let it sit, covered, for 5 minutes.
Fluff the cooked rice with a fork.
In a separate saucepan, heat the milk and butter over medium heat.
Stir in the shredded cheese until melted and smooth.
Combine the cheesy mixture with the fluffed rice.
Season with salt and pepper to taste.