Soak the dried beans and cook over a slow flame. In a pan, gently fry the onion, sliced. Add the other vegetables, diced, with the exception of the cabbage, kale and beans which are added at a later point.
When the vegetables have sweated out their juice, cover with hot water and then add all the cabbage and kale, shredded. Cover and simmer for an hour over medium heat. Add the cooked beans (some of them whole and some pourèed), salt and pepper.
Leave to simmer for another 20 minutes, stirring frequently because the beans tend to stick to the bottom of the pan. Add two or three tablespoons of tomato purèe.
Slice the Stale bread and, in an earthenware casserole, alternate layers of bread with the soup until the bread is well impregnated. Leave to stand for a day. To serve, remove the desired quantity from the casserole and heat it up or "re-boil" it as the name in Italian suggests.