Preheat the oven to 160C/140C Fan/Gas 3.
In a large ovenproof pan or casserole, heat 100g/3½oz butter and the oil. Add the pork fat-side down and cook until golden-brown and crisp.
Remove the pork from the pan and set aside. Fry the garlic and sage for 1-2 minutes. Add the lemon zest, squeeze in the juice and drop in the rest of the lemon. Add the milk and bring to the boil.
Season the pork shoulder with salt and freshly ground black pepper. Put it, fat-side up, into the hot milk. Add the potatoes and cook in the oven for 1½ -2 hours, or until the pork is very tender.
To cook the cavolo nero, heat the remaining butter in a large frying pan. Once hot, add the cavolo nero and a few tablespoons water. Cook until wilted.
Remove the pork from the sauce carefully and slice thickly. Place on serving plates, pour over the sauce and serve with the cavolo nero.