Trim fat from meat. Cut into 1 inch pieces. In a 4 quart slow cooker, mix meat, onion, Worcestershire sauce, bouillon granules, garlic, oregano, basil and thyme.
Cover and cook on low heat setting for 10 to 12 hours or on high heat setting for 4 to 6 hours. Stir to break up meat cubes. If using low heat setting, turn to high heat setting. Stir in pepperoncini. Cook, uncovered on high heat setting for 30 minutes more stirring often to break up meat.
Preheat broiler. Using a slotted spoon, place meat on the bun bottoms. Top with cheese. Place bun bottoms with meat on baking sheet. Broil 4 to 5 minutes from heat about 1 minute or until cheese is melted and bubbly. Cover with bun tops.