Heat the oven to 375°F and add the rice and black beans to a 9-by-13-inch baking dish.
Stir in the salsa, vegetable broth, salt and black pepper until the rice is evenly spread and submerged.
Cover the dish tightly with foil and bake for 45 to 50 minutes.
Remove the foil and test several grains near the center; return the covered dish for 5 minutes if they remain chalky.
Scatter the cheddar over the tender rice and bake uncovered for 8 to 10 minutes, until melted.
Rest the bake for 10 minutes before scooping so the rice can absorb the remaining sauce.