1. Combine the first 7 ingredients in a 6-qt. electric pressure cooker. Lock lid; close pressure-release valve. Adjust to pressure-cook on high for 10 minutes. Quick-release pressure. Add peppers and pepper rings. Lock lid; close pressure-release valve. Adjust to pressure-cook on high for an additional 5 minutes. Let pressure release naturally for 10 minutes; quick-release any remaining pressure.
2. Place bun bottoms on ungreased baking sheets, cut sides up. Using tongs, place beef, vegetables and cheese on bun bottoms. Broil 3-4 in. from heat until cheese is melted, 1-2 minutes. Add bun tops; serve with cooking juices.
3. Slow-cooker option: Combine the first 7 ingredients in a 4- or 5-qt. slow cooker. Cook, covered, on low 6 hours. Stir in peppers and pepper rings; cook, covered, 1-2 hours or until meat is tender.
4. Place bun bottoms on ungreased baking sheets, cut sides up. Using tongs, place beef, vegetables and cheese on bun bottoms. Broil 3-4 in. from heat until cheese is melted, 1-2 minutes. Add bun tops; serve with cooking juices.