1. Combine 1/4 cup onion, pepper, salt, garlic, and beef. Shape into 4 (1/2-inch-thick) patties. Heat a skillet over medium-high heat. Coat with cooking spray. Add patties; cook 3 minutes on each side or until browned.
2. Melt butter in pan. Add mushrooms; sauté 4 minutes. Stir in wine and remaining onion; cook 2 minutes. Combine broth and flour; add to pan, and bring to a boil. Cook 5 minutes or until thick. Add patties and vinegar to pan; cook 2 minutes.
If you're cooking for kids, omit the wine and replace with more beef broth.