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Place the onions in a five-quart or larger slow cooker. Stir in the butter, oil, salt, and a generous amount of pepper.
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Cover and cook on the low setting overnight, until the onions are a dark golden-brown and soft, 12 hours or overnight.
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Stir in the broth and vinegar.
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Cover and continue cooking on the low setting for six to eight hours. This is flexible; as long as your slow cooker holds moisture well (wrap a towel over the lid if quite a lot of steam escapes), you can cook the soup for hours. Longer cooking will only intensify the flavors. Taste and season with more salt and pepper if needed, and stir in the brandy if using.
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Arrange a rack in the upper third of the oven and heat to 350°F. Ladle the soup and onions into oven-safe soup bowls and place the bowls on a rimmed baking sheet.
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Top each bowl with a slice of toast and a generous quantity of shredded Gruyère cheese, about 1/3 cup per bowl.
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Bake until the cheese is completely melted, 20 to 30 minutes.
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Turn the oven to broil. Broil until the cheese is bubbling and browned, about two to three minutes. Remove from the oven and let cool for a few minutes. Serve with chopped fresh shallot or onion if desired