Step 1: In a large pot or Dutch oven, heat olive oil over medium heat. Add chopped onion and cook until softened, about 5-7 minutes.
Step 2: Stir in minced garlic and cook for another minute until fragrant.
Step 3: Pour in the beef broth, diced tomatoes, and chopped sauerkraut. Bring to a simmer, then reduce heat, cover, and let it cook for 15 minutes to allow flavors to meld.
Step 4: Add the diced corned beef and cook for 5 more minutes.
Step 5: In a separate bowl, whisk together the heavy cream and softened cream cheese until smooth. Gradually stir this mixture into the soup.
Step 6: Stir in the Dijon mustard and caraway seeds. Season with salt and black pepper to taste. Heat through gently, but do not boil after adding cream.
Step 7: Ladle the creamy Reuben soup into bowls. Garnish with shredded Swiss cheese, rye bread croutons, and fresh parsley, if desired. Serve hot.