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Boil the pasta. Meanwhile, put the walnuts and garlic in a food processor and whizz until finely chopped. Add the basil, cheese, butter and oil and pulse a few more times. Season.
Pour the cream into a pan and warm through. Add two-thirds of the pesto, then gently heat to loosen it. When the pasta is ready, drain, reserving 2 tbsp of the cooking water, then mix both with the sauce. Serve immediately, sprinkled with the extra Parmesan and basil, if using. The leftover pesto will keep in the fridge for up to a week, or frozen for up to a month.