If you want to substitute ingredients from your pantry for the Bloody Mary Mix, I think that diced tomatoes, carrots, celery, onions, garlic, lime juice, horseradish, celery seeds (and/or celery salt), molasses, and hot sauce would be a good start. You can even add some gluten-free Worcestershire sauce if you find one that meets your needs (e.g., vegan). You could also use a spicy vegetable juice (ready-made or homemade) in combination with diced or pureed tomatoes in place of the Bloody Mary mix for a soup with less complex flavors. I’d definitely recommend the use of an immersion blender near the end of your cooking time if you are adding diced or larger pieces of tomatoes. The finely shredded cabbage in this recipe creates a nice crunchy “noodle” effect.