Heat the oven to 375°F and coat a 9-by-13-inch baking dish with cooking spray.
Stir the converted rice, ham, broccoli, broth, milk, onion powder and black pepper together in the dish.
Press the rice under the liquid, seal the dish tightly with foil and bake for 40 minutes.
Test grains from the center; if they are firm, stir in 2 tablespoons hot broth, reseal and bake for 5 to 10 minutes more.
Fold the cheddar into the tender rice until it melts through the sauce.
Rest the casserole for 8 minutes before serving.