Cut the pork into strips about 1/2 inch long and 1/4 inch wide.
Put oil, butter, onion, and pork in a soup pot over medium heat. Stir from time to time.
When the onion turns a deep gold, add the diced vegetables, shredded cabbage, and the fresh beans or the soaked dried beans. Stir about a minute to coat well.
Add tomatoes with their juice, a pinch of salt, and several grindings of pepper. Stir, then add the broth. If it does not cover the ingredients by at least 1 inch, add water to make up the difference.
Cover, lower the heat to a very slow simmer, and cook at least 2 hours. The finished soup should be thick. Taste and adjust salt and pepper. Serve with Parmigiano at the table.