Heat the oven to 375°F and grease a 9-by-13-inch dish.
Heat the oil in a skillet and brown the mushrooms for 7 minutes. Add the beef and onion, cook until browned and drain; add garlic for 30 seconds.
Stir the rice, beef mixture, broth, milk, Worcestershire, thyme, salt and pepper together in the dish.
Cover tightly with foil and bake for 45 to 50 minutes, until the rice is tender and most liquid is absorbed.
Remove the foil, fluff gently, sprinkle with cheddar and bake uncovered for 5 minutes. Rest 10 minutes.