1. Cut 1 onion into quarters; set aside remaining onion. In 5- to 6-quart saucepot or Dutch oven over high heat, heat beef chuck short ribs, cut-up onion, 1 teaspoon salt, and enough water to cover to boiling. Reduce heat to low; cover and simmer 1 1/4 hours or until short ribs are fork-tender. Remove ribs to platter. If not using ribs right away, cover and refrigerate.
2. About 45 minutes before serving, prepare barbecue sauce: Dice green pepper and reserved onion. In 2-quart saucepan over medium heat, in hot salad oil, cook green pepper and onion until tender, stirring occasionally. Stir in catchup, brown sugar, Worcestershire, hot-pepper sauce, 1/3 cup water, and 1/4 tea spoon salt; over high heat, heat to boiling. Reduce heat to low; cover and simmer 5 minutes to blend flavors.
3. Preheat broiler if manufacturer directs. Arrange short ribs on rack in broiling pan. About 5 inches from source of heat, broil short ribs about 20 minutes or until heated through, brushing with barbecue sauce and turning short ribs occasionally