Put the cubed potato, the finely chopped onion and the sausage pieces in a large saucepan and add the bacon cooking water, the chicken stock or the water, whichever you are using. Add a little salt and freshly ground black pepper - but don't add too much salt if you're using bacon cooking water. Place over a medium heat and bring to a boil, then simmer for about 30 minutes, until the potatoes are just tender.
Add the torn leftover boiled or fried bacon, whichever you're using, and cook for another few minutes. Stir in the finely chopped fresh parsley, season with more salt (if necessary) and freshly ground black pepper to taste, and serve immediately.