Cook the pasta in boiling salted water according to packet instructions. 10 minutes from the end of cooking time, add the potato to the pasta.
To make the pesto, blitz the first four ingredients in a food processor to make a paste, then add enough oil to loosen to a swampy consistency. Add a little salt and set aside. 5 minutes from the end of the pasta cooking time, add the green beans. Warm deep plates in the oven at a low temperature with 2tbsp pesto in. Drain the pasta and vegetables, reserving a little of the cooking water, and return to the pan.
Toss the pasta and vegetables with butter. Divide the pasta and vegetables between the two serving plates and toss with the pesto and a little of the cooking water to loosen to a sauce. Serve with more Parmesan if desired.
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