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Heat 1½ tbsp oil in a large pan or flameproof casserole dish over a low-medium heat. Add the onion, celery and carrots with a pinch of salt. Cook for 10 mins, stirring occasionally, until softened but not coloured. Transfer to a plate using a slotted spoon.
Pour the remaining oil into the pan, increase the heat and tip in the pancetta. Cook for 3-4 mins until golden. Add the mince and chicken livers, and cook for a further 5 mins until browned, breaking down the mince with the back of a wooden spoon.
Return the vegetables to the pan and add the bay leaf and tomato purée. Cook for a 1 min more and mix well. Pour in the wine and reduce by half. Add the stock and passata with some seasoning and bring to the boil. Reduce the heat to medium and let the sauce bubble away for 35-40 mins, stirring occasionally, until reduced by half and you are left with a thick ragu.
Bring a large saucepan of salted water to the boil 15 mins before the sauce is ready. Drop in the pasta, cook following pack instructions until al dente, then drain.
To finish the sauce, stir in the milk and season to taste. Tip the pasta onto a plate and top with the Bolognese. Serve with the Parmesan.