Heat the oven to 375°F. Brush pepper halves with oil, arrange cut-side up in a 9-by-13-inch baking dish and bake for 15 minutes to soften slightly.
Meanwhile, brown beef and onion in a skillet for 7 to 8 minutes until the meat reaches 160°F. Drain excess fat.
Add tomato sauce, ketchup, Worcestershire, vinegar, brown sugar, salt and pepper. Simmer for 8 to 10 minutes until thick.
Divide the hot filling among the pepper halves and scatter cheddar over each. Bake for 15 to 20 minutes more until the peppers are tender and the cheese melts.
Rest for 5 minutes, then lift with a wide spatula and serve two pepper halves per person.