Melt 1/4 cup butter in a large, oven-safe Dutch oven on medium heat. Stir in onions until they are all coated in butter. Transfer skillet to the preheated oven and cook onions, stirring occasionally, until they are tender and well browned, about 1 hour.
Transfer the Dutch oven to the stovetop; cook and stir onions over medium heat until they start to brown and stick to the bottom of the pan, about 5 minutes. Pour sherry and vinegar into the pan, and bring to a boil while scraping browned bits of onion off the bottom of the pan with a wooden spoon.
Pour in chicken broth, beef broth, thyme, and Sunny Paris. Bring to a boil, skimming off any foam and fat that appear on top. Reduce heat to low and simmer for about an hour. Season with salt and pepper to taste.
Preheat the oven's broiler and set the oven rack about 6 inches from the heat source.
Put a slice of swiss and cheddar cheese on each slice of bread. Put the slices of bread on a boiling pan, and put the slices of bread in the broiler for about 3 minutes, or until the cheese has melted. Serve the bread with the soup, and enjoy!
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