To prepare the soup, start by heating olive oil in a large stock pot over medium-high heat. Once the oil is hot, add the diced onion and carrot and sauté for 7-9 minutes, or until they have softened.
Next, add the minced garlic and diced corned beef to the pot and cook for an additional 1-2 minutes until fragrant. Season the mixture with salt, pepper, and oregano.
Pour the chicken stock into the pot, then stir in the sauerkraut. Bring the mixture to a boil, then reduce the heat and let it simmer for 20 minutes.
While the soup simmers, prepare the slurry by whisking cornstarch and cold water together in a small bowl. Once the bay leaf has been removed from the soup, whisk in the slurry and continue cooking for another 5-10 minutes, or until the soup has thickened.
To finish the soup, stir in the heavy cream and Swiss cheese, and cook for an additional 5 minutes, or until everything is heated through. Once the soup is ready, ladle it into serving bowls and top each bowl with rye bread croutons. Serve hot and enjoy!