Step 1

Season the onions. Place the onions in a 5-quart or larger slow cooker. Stir in the butter, oil, salt, and a generous amount of pepper.

Step 2

Cook on LOW for 12 hours. Cover and cook on the LOW setting overnight until the onions should be dark golden-brown and soft, 12 hours or overnight.

Step 3

Add the broth and vinegar. Stir in the broth and vinegar.

Step 4

Cook for LOW 6 to 8 hours. Cover and continue cooking on the LOW setting for 6 to 8 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.

Step 5

Portion the soup into oven-safe bowls. 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.

Step 6

Top with toast and shredded cheese. Top each bowl with a slice of toast and a generous quantity of shredded Gruyère cheese, about 1/3 cup per bowl.

Step 7

Bake for 20 to 30 minutes. Bake until the cheese is completely melted, 20 to 30 minutes.

Step 8

Broil for 2 to 3 minutes. Turn the oven to broil. Broil until the cheese is bubbling and browned, 2 to 3 minutes. Remove from the oven and let cool for a few minutes. Serve with chopped fresh shallot or onion if desired.