If using pork rind: cover it with cold water by about 1 inch, bring to a boil, cook 1 minute, drain, cool, then cut into strips about 1/2 inch wide and 2 to 3 inches long. If using pig’s feet or hock: boil covered in water that covers by about 2 inches for 45 minutes to 1 hour. Bone, cut into strips about 1/2 inch wide, and set aside.
Put olive oil, onion, and pancetta in a soup pot over medium heat. Cook the onion, stirring, until translucent. Add the chopped garlic and cook, stirring now and then, until lightly colored.
Add cabbage, celery, the pork, drained tomato, and thyme. Cook over medium-low heat until the cabbage fully wilts, stirring thoroughly from time to time.
Add broth, salt, and several grindings of pepper. Cover, lower heat, and cook very gently about 2 1/2 hours.
Uncover and skim off as much surface fat as you can. Bring back to a slow simmer.
Prick the sausages, brown them in a skillet over medium-low heat using only their own fat, then add the browned sausages to the pot, leaving the skillet fat behind.
Purée half the drained cooked or canned beans into the pot and stir well. Cover and simmer 15 minutes.
Add the remaining whole beans. If you want it looser, add a little more broth or water. Cover and simmer 10 minutes more. If stopping here for make-ahead, bring the soup to a simmer for a few minutes before finishing later.
Make the flavored oil: warm mashed garlic in olive oil over medium heat until the garlic turns light nut brown. Add rosemary, turn off heat, stir a couple of times, then strain the oil into the pot, discarding garlic and rosemary.
Simmer briefly and serve. Offer optional grilled or toasted bread.
