Saute onion bell peppers, mushrooms and garlic in olive oil over medium-high heat until golden brown. Reduce heat and continue to cook until tender, stirring occasionally. Stir in sugar, oregano, vinegar and salt. Add cheese and cook, stirring constantly, until cheese melts.
Combine the beef broth and sliced beef in a bowl and microwave until hot.
Place 3 ounces beef mixture in each bun and top with cheese mixture. Serve immediately.