In a large soup pot, sauté the onions and celery in the olive oil over medium heat, stirring occasionally, until starting to color, about 3 minutes. Stir in the carrots, potatoes and garlic, and cook another2 minutes.
Add the kale, cabbage, crushed tomatoes, thyme, bay leaves, salt and water. Stir and bring to a simmer.Then cover and cook on low heat for around 30 minutes.
In a separate bowl, use an immersion blender to blend half the beans into a smooth thick paste, about 2 to 3 minutes. If needed, borrow just enough of the cooking water necessary to facilitate blending. Add the puréed and whole beans to the soup, and cook for another 15 minutes. Adjust salt to your taste.
Assemble for Ribollita
To Serve Now: Cut or tear the bread into bite-sized pieces and place at the bottom of a soup pot. Ladle the soup over it and bring to a boilover medium heat. Cook, stirring occasionally, until warm, about 10 minutes. (You can add water if you like it more soupy or let it boil down to make it thicker.) Cover, take off the heat, and let rest 10 minutes before serving.To Serve Later (for the best ribollita): Add a large slice of bread to the bottom of a soup pot (if you like, rub the bread with a peeled clove of garlic first), then cover with a ladle of soup. Repeat with the remaining slices of bread and soup. Let cool, then refrigerate 4 hours to overnight (or portion and freeze*). When ready to serve, bring just to a boil, then cook over medium heat, stirring occasionally, until warm, about 10 minutes.
Serve with a generous drizzle of olive oil and freshly cracked pepper.
Variations
Greens - Purée a small portion of the greens along with the beans, if you like.
Red onion - Sprinkle chopped red onion over the bread-thickened soup right before rewarming.
Rewarming - You can also rewarm the bread-thickened soup in a skillet or in the oven. It doesn't have to be in a pot.
Storing
Keeps well in an airtight container in the refrigerator for up to 5 days, and in the freezer for up to 3 months. *Thaw before rewarming.
Tools
Immersion Blender, food processor, blender, or potato masher