Heat butter and oil in heavy, large saucepan over medium heat. Add onions, garlic and salt, and cook 5 minutes, stirring often. Reduce heat to very low, and cook, stirring occasionally, 50 to 60 minutes, until onions are very tender and brown.
Stir in flour, and cook 3 to 4 minutes, stirring constantly. Blend in broth, sherry and mustard. Cover, and simmer 15 minutes, stirring occasionally. Stir in sherry vinegar.
Preheat broiler, ladle soup into six heat-proof bowls. Top each with slice of toast and grated cheese. Broil until cheese is bubbly and golden, about 1 to 2 minutes. Serve hot.