Melt the butter in a large pot or Dutch oven over medium heat. Add the diced onion and cook for 3–4 minutes, until softened. Add the garlic and cook for about 30 seconds.

Sprinkle the flour over the onion mixture and stir well. Cook for about 1 minute, stirring constantly.

Gradually whisk in the beef broth to prevent lumps. Add the milk or cream and stir until well combined.

Stir in the corned beef, sauerkraut, and caraway seeds, if using. Bring the soup to a gentle simmer and cook for about 5 minutes, stirring occasionally.

Reduce the heat to low. Stir in the shredded Swiss cheese a little at a time until melted and the soup is creamy and smooth. Do not let the soup boil after adding the cheese.

Taste and add salt and pepper as needed. Ladle into bowls and top with Thousand Island dressing, rye croutons, additional sauerkraut, and chopped dill or parsley.