Heat the oil in a large non-stick saucepan or large flame-proof casserole and fry the onion and garlic gently for 5 minutes, or until softened but not coloured, stirring occasionally. While the onion is frying, cut the carrots, turnips, potatoes and parsnip into roughly 1.5cm/¾in chunks.
Add the root vegetables to the pan with the onion and garlic and cook over a low heat for 5 minutes, or until beginning to soften, stirring occasionally. Stir in both the sweet and smoked paprika and fry for a few minutes. Add the tomatoes and the tomato purée into the pan, increase the heat a little and cook for 2–3 minutes, stirring regularly.
Add the chorizo, Puy lentils and the stock into the pan and bring to the boil. Reduce the heat and simmer gently for 45 minutes, or until the vegetables and lentils are tender, stirring every now and then.
Add the cavolo nero, kale or spring greens to the pan with the vegetables. Cook for 5 minutes or until softened, stirring regularly.
Season the soup with salt and lots of freshly ground black pepper. Serve in deep bowls, with a dollop of soured cream or crème fraîche and a sprinkling of paprika.