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Boil the kettle. Put all the ingredients except the pecorino and basil in a wide saucepan or deep frying pan and season well. Pour over 800ml kettle-hot water and bring to a simmer, using your tongs to ease the spaghetti under the liquid as it starts to soften.
Simmer, uncovered, for 10-12 mins, tossing the spaghetti through the liquid every so often until it is cooked and the sauce is reduced and clinging to it. Add a splash more hot water if the sauce is too thick or does not cover the pasta while it cooks. Turn up the heat for the final few mins to drive off the excess liquid, leaving you with a rich sauce. Stir through the pecorino and basil, and serve with an extra drizzle of oil and pecorino on the side.