Wash the rapini and cut off the florets, saving them for another day or add them to the soup with the stalks. Remove the tough stems from the rapini leaves and reserve. Stack the leaves, then cut them into thin strips and set aside. Rinse the can of beans.
In a large pot, add the broth, water, sausage, potatoes, rapini stems that have been reserved, beans and seasonings then simmer until the potatoes are almost tender. At this point, remove the rapini stems and discard. Add the chopped rapini leaves to the soup, and simmer on med/ low until the rapini is cooked. Adjust for salt and pepper if desired.
If you like, you can slice the chorizo sausage into slices and add it back to the finished soup. I like to serve mine on the side, allowing people to add what they like.