Chop the garlic, onions, celery, carrots, potatoes, beans and zucchini into small pieces.
Heat the butter and oil in a large saucepan and fry the bacon for 2 minutes. Add garlic and onions, fry for 2 minutes, then stir in celery, carrots and potatoes and fry for another 2 minutes. Put the beans in the saucepan and fry for 2 minutes. Stir in the zucchini and fry for another 2 minutes. Put the lid on and simmer the vegetables for 15 minutes, stirring occasionally.
Add the stock, tomatoes, tomato paste, basil and cheese rind and season to taste. Bring to the boil, reduce the temperature and simmer gently for 1 hour. Remove the rind and discard. Put the spaghetti pieces in the saucepan and cook for 10 minutes.
Serve in large, preheated soup plates sprinkled with freshly grated Parmesan.