Soak the cannellini beans with 1 tablespoon (14g) of the salt in around 1.5l of water overnight.
The next day, drain and rinse the beans and add them to a large pan with 2l of water. Peel and add the whole garlic cloves as well as the sprigs of sage. Bring to a boil, skim off any foam, then reduce the heat and simmer with the lid left slightly ajar for 1 hour or until just tender. Alternatively, cook with the garlic, sage and just 1l of water for around 10 minutes in a pressure cooker. Remove the sage, then drain the beans and garlic but keep the cooking liquid. When the beans have around 25 minutes left, heat the olive oil in a casserole over medium-low heat. Peel and dice the onion, then dice the carrot and celery, adding them to the casserole as you go. Strip the cavolo nero leaves and set aside, then dice the stalks and add them to the casserole as well along with the chilli flakes, black pepper and the remaining 1¼ tablespoons (18g) of salt. Cook until the veg has softened (10-15 minutes).
Meanwhile, chop the cavolo nero leaves into strips. Transfer a quarter (about 180g) of the beans with the cooked garlic and around 250ml of the bean cooking liquid to the jug of an immersion blender and blend until smooth. Then measure the remaining cooking liquid and add enough fresh water to reach 1.25l.
Add the tomato paste to the casserole and give it a stir to mix it through, then add the cavolo nero leaves along with the blended beans, the cooked beans and the 1.25l liquid. Return to a boil, then reduce the heat and simmer covered for 20 minutes.
Slowly sprinkle in the polenta, stirring constantly to avoid lumps. Cook uncovered until the polenta is soft (1-2 minutes), then turn off the heat and leave to sit covered for 5 minutes, during which the soup will thicken more.
Divide over bowls and serve with an extra drizzle of olive oil and a sprinkle of black pepper.