Heat the oven to 375°F and spread the rice across a 9-by-13-inch baking dish.
Add the chicken, frozen broccoli, salt and black pepper and distribute them evenly through the rice.
Pour in the broth and press every grain below the liquid.
Cover the dish tightly with foil and bake for 50 minutes without opening the oven.
Remove the foil, check that the rice is tender and the chicken reaches 165°F, and sprinkle the cheddar over the top.
Bake uncovered for 10 to 15 minutes more, until the cheese bubbles, then rest for 10 minutes.