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Cook the linguine. Meanwhile, tear the ham into small pieces and fry in the olive oil until golden and crisp.
Drain the pasta, reserving a little of the cooking water, then return to the pan. Tip in the cooked ham. Mix together the lemon juice, egg yolks and crème fraîche, then add this to the pan along with the basil and Parmesan. Mix in with tongs, adding a little of the cooking water, if needed, to make a creamy sauce that coats the pasta. Serve with extra Parmesan grated over the top, if you like.