Soak the beans overnight in cold water, using a separate bowl for each type of bean.
Rinse and drain the beans, then boil them in separate pans; the borlotti beans for about an hour, the cannellini beans for 45 minutes. Drain and set aside.
Meanwhile, cook the soffritto. Heat the olive oil in a saucepan and gently fry the celery, carrot, onion, garlic, rosemary and bay leaves until golden, about 15 minutes.
Remove the rosemary sprig and bay leaves and season with salt and freshly ground black pepper.
Add the ham fat or bone and the cannellini beans to the soffritto. Season with salt and freshly ground black pepper, and cook for a further 10 minutes.
Add the stock and bring to the boil, then simmer for 25 minutes or until the beans are tender.
Remove the pieces of ham fat or bone. Stir in the whole borlotti beans. Season with more salt and freshly ground black pepper to taste. Serve drizzled with extra virgin olive oil.