Soak the Dried cannellini beans in plenty of cold water overnight (or use a quick-soak: cover with water, bring to a boil for 2 minutes, then turn off and let sit 1 hour), then drain.
Place the drained beans in a large pot, cover with fresh water or a little Vegetable stock, add the Parmigiano Reggiano rind and a sprig of Rosemary, and simmer gently until the beans are tender, about 1–1½ hours; salt near the end of cooking. Reserve a generous cup or two of the cooking liquid before draining.
Meanwhile, chop the Onion, Carrots, and Celery finely, mince the Garlic, dice the Potato into small cubes, tear the Tuscan-style country bread into bite-sized pieces, and thinly slice the Cavolo nero (Tuscan kale), removing any very tough stems.
In a wide, heavy pot, heat a couple of tablespoons of Extra-virgin olive oil over medium heat. Add the chopped onion, carrots, and celery and cook, stirring, until softened and beginning to brown, about 8–10 minutes.
Add the garlic and cook another minute until fragrant. Stir in the Canned peeled tomatoes, breaking them up with the spoon, then add the cooked beans, some of their reserved cooking liquid, and enough Vegetable stock to give you a soupy consistency. Add the diced potatoes.
Bring the pot to a simmer and cook until the potatoes are tender, about 15–20 minutes. If the soup seems too thick, add a little more reserved bean liquid or stock.
Stir in the sliced cavolo nero and the torn bread pieces, pushing them down so they soak in the broth. Simmer, stirring occasionally, until the bread has mostly broken down and the kale is tender, about 10–15 minutes. Use the back of a spoon to mash a few beans and bread against the pot to thicken the soup and create a creamy texture.
Remove and discard the Parmigiano rind and any large rosemary stems. Season to taste with Salt and Black pepper. Finish with a drizzle of extra-virgin olive oil and serve hot—Ribollita always tastes even better the next day after the flavors rest.
