In a dutch oven, saute sliced onions in butter until soft. Stir in flour to form a paste; pour in bourbon, stirring until smooth. Gradually stir in broth; season with basil and simmer 30-40 minutes. Drop into bottom of each soup bowl a slice of toasted French bread, fill with onion soup and sprinkle with cheese. Broil until cheese is golden and bubbly. Serve immediately.