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Heat the oil in a large saucepan and add the onion. Cook over a gentle heat for 8-10 mins until the onion softens. Add the cauliflower, milk and stock. Bring to a simmer, cooking for 10-12 mins until the cauliflower is tender.
Add the cream, season well and bring back to the boil. Take off the heat, throw in the chestnuts and blend with a hand blender until smooth. Taste and add more seasoning, if you like. To serve, top with shaved Parmesan, black pepper and a drizzle of olive oil.