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In a large stockpot, heat olive oil over medium-high. Add onion and carrots, sautéing until softened, about 7-9 minutes.
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Add garlic and corned beef, cooking an additional 1-2 minutes until fragrant. Season with salt, pepper, and oregano.
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Pour in the chicken stock and add sauerkraut. Bring the mixture to a boil, then reduce heat and simmer for 20 minutes.
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In a small bowl, whisk together cornstarch and cold water to create a slurry. Remove the bay leaf from the soup, then whisk in the slurry. Continue cooking for 5-10 minutes until the soup thickens.
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Stir in heavy cream and Swiss cheese, cooking until heated through, about 5 more minutes.
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Serve hot, topping each bowl with rye bread croutons.