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Set aside two handfuls of small cauliflower florets. Heat the butter in a large pan, add the shallots and gently fry until soft but not brown. Add the cauliflower, potatoes, milk and stock. Season and bring to the boil, then reduce the heat, cover and gently simmer for 15-20 mins until the vegetables are tender. Purée until smooth either with a stick blender or in a food processor (you will need to do this in batches). Return to the pan and add the cream. Warm through and add more seasoning if necessary.
Heat the oil in a pan, add the reserved cauliflower florets and fry until brown and starting to soften. Add a splash of water, cover and cook for a further 1-2 mins until just tender. Tip the cauliflower into a bowl. Add the chorizo to the pan and fry quickly on each side until crisp. Drain on kitchen paper.
Serve the soup in bowls with a small pile of crisp cauliflower in the centre, topped with a couple of slices of chorizo and scattered with coriander.