Drain the soaked cannellini beans and place them in a pot with the bay leaf, the smashed garlic clove, and enough fresh cold water to cover by 2 inches. Bring to a gentle simmer and cook uncovered for about 60 to 75 minutes, until the beans are fully tender but not falling apart. Season with a pinch of salt in the last 10 minutes. Do not drain; reserve the beans in their cooking liquid.

Pass about one third of the cooked beans, with some of their liquid, through a food mill or mash them thoroughly with a potato masher to make a thick puree. Set the whole beans and the puree aside separately, keeping all the bean broth.

In a large heavy pot, warm the extra-virgin olive oil over medium-low heat. Add the onion, carrots, and celery and cook slowly, stirring often, for 15 to 20 minutes, until very soft, sweet, and lightly golden. Do not rush this soffritto; it is the foundation of the soup.

Stir in the minced garlic, rosemary sprig, and thyme sprigs and cook for 2 minutes, until fragrant. Add the crushed tomatoes with their juice and cook for 5 minutes, stirring, until the tomato darkens and loses its raw smell.

Add the shredded savoy cabbage and cavolo nero to the pot in handfuls, stirring to wilt each batch before adding the next. Cook for 10 minutes, until the greens are collapsed and glossy.

Pour in the bean puree, the whole beans, all of the reserved bean cooking liquid, and enough water to just cover the vegetables, about 8 cups total liquid. Add the kosher salt and black pepper. Bring to a gentle simmer and cook uncovered for 45 minutes, stirring occasionally, until the soup is deeply flavored and slightly thickened.

Remove the rosemary and thyme stems. Tear the stale Tuscan bread into thick chunks and stir them directly into the hot soup. The bread should fully submerge and begin to melt into the liquid. Simmer for 10 more minutes, stirring gently, then turn off the heat.

Cover the pot and let the soup rest at room temperature for at least 2 hours, or ideally refrigerate overnight. This resting step is essential; the bread absorbs the broth and the soup becomes thick and almost stew-like.

The next day, return the pot to low heat and reboil (ribollita) the soup gently for 20 to 25 minutes, stirring often and adding a splash of water only if it threatens to scorch. The finished soup should be thick enough that a spoon almost stands up in it.

Ladle into warm bowls and finish each serving with a generous drizzle of raw Tuscan extra-virgin olive oil and a grind of black pepper. Serve immediately, with thinly sliced raw red onion on top if desired.