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Melt the butter in a large saucepan over a medium heat. Add the coriander and the vegetables, fry for 4-5 mins, then cover with 400ml water and bring to the boil. Cook until all the vegetables are soft – around 20-25 mins.
Season with salt, pepper and nutmeg, then add the milk. Transfer to a blender or blitz with a stick blender until smooth, then return to the pan to heat through. (For a really smooth consistency, push the mixture through a sieve after blending.) Check the seasoning and add a little more salt and nutmeg, if you like.
Meanwhile, heat the cooked haggis or black pudding in a frying pan until sizzling. Serve the soup in bowls and top with the haggis or black pudding, a swirl of double cream and the celery leaves.