Melt the salted butter and olive oil in a 10 quart stock pot on medium heat. Sauté celery, carrots, onion, prosciutto, and garlic and cook until soft about 5 minutes.
Add the chopped green beans, cabbage, zucchini, parsley and basil and cook for about 10 minutes or until soft.
Add chicken stock, bay leaf, diced tomatoes, Pecorino Romano rind and potatoes. Bring the soup to boil and then reduce to a simmer. Simmer for 30 minutes or until potatoes are soft.
Add canned garbanzo, kidney, and cannelini beans and simmer for 5 additional minutes.
Remove the Pecorino Romano rind and prosciutto (if you kept it whole). Stir in the grated Pecorino Romano cheese, stirring constantly until melted in. Ladle evenly among bowls.