Prepare the Vegetables: Soak zucchini and green beans in cold water (optional), rinse, and dice all vegetables.
Sauté the Base: Heat olive oil and butter in a large stockpot. Add sliced onions and sauté until golden.
Layer the Vegetables: Add carrots and cook for 2-3 minutes. Repeat this process with celery, potatoes, fresh beans, zucchini, green beans, and finally shredded cabbage.
Add Liquid: Pour in the broth, canned tomatoes with juice, Parmesan rind, and a pinch of salt. Stir well.
Simmer: Cover the pot and simmer at a slow boil for at least three hours. If the soup becomes too thick, add more water or homemade broth.
Add Beans: Fifteen minutes before the soup is done, stir in canned or cooked dry beans.
Finish with Parmesan: Remove the Parmesan rind, stir in grated cheese, and adjust salt to taste.