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Warm the olive oil in a heavy-based pan over a medium-low heat and add the onion, carrot, celery, garlic and a big pinch of salt. Cover and cook, stirring occasionally, for 12-15 minutes until the veg is completely soft and sweet.
Meanwhile, bring a deep pan of salted water to the boil and blanch the cavolo until tender, about 5-6 minutes, then take off the heat, drain (you can roughly chop it with scissors while in the sieve, but keep the water).
Stir the tomatoes into the veg, breaking them up with a spoon, and cook for a further 10 minutes. Add the beans (and any cooking water if cooked from fresh) and cook for a further few minutes. Using a hand blender, purée about a quarter of the mix while still in the pan to thicken it up (or remove 3 ladlefuls and blitz in a blender), then return to the pan.
Scoop in the cavolo and pour over enough of its cooking water to just cover the veg. Season, then bring to a simmer for 5-10 minutes to unite everything, then turn off the heat. Transfer to bowls and drizzle each portion with plenty of nice extra virgin olive oil. Keeps for a week in the fridge and will just get better and better.
Tip: I usually make this with canned beans BUT if you are able to plan in extra time to soak and cook some dried beans, adding their cooking liquid to this soup takes it to whole new dimensions.