In a large pan, heat butter and olive oil over medium heat.
Brown the bacon, garlic, and onions until fragrant and golden.
Transfer the bacon mixture to a large pot and add potatoes, carrots, celery, zucchini, cabbage, cannellini beans, chopped tomatoes, salt, pepper, and stock.
Bring the mixture to a boil over high heat.
Reduce heat to low and simmer for 40 minutes until vegetables are tender.
Add ditalini pasta and cook for an additional 10 minutes until pasta is al dente.
Ladle into bowls and sprinkle fresh grated Parmesan cheese over each serving.