First make the pesto:
Finely chop the nuts and place in a bowl, then finely chop the parsley leaves and add to the nuts. Place the garlic, goats cheese and lemon zest and juice in the bowl and pour in the olive oil stirring as you go until you have a thick, sloppy puree. Taste and season to taste.
Bring a very large pan of water to the boil and salt well. Meanwhile, cut the potatoes into thick matchsticks (the size of thin chips). Add the potatoes and pasta to the pan and cook until the pasta is al dente – probably 10-12 minutes, which should be the right amount of time for the potatoes too. If the pasta is a type that cooks very quickly, put the potatoes in a few minutes before. (If using very freshly dug new spuds, they’ll cook quicker, 6-7 minutes, so add halfway through the pasta cooking). In the meantime, cut the beans into lengths that roughly match the size of the pasta. Add them to the pan about 4 minutes before the end of cooking.
Drain the pasta and vegetables, and let them steam off for a minute or two, then add the pesto and mix thoroughly but gently. Check the seasoning (it will probably benefit from a good grinding of black pepper).
Divide between warmed serving bowls, scatter with extra cheese if you wish.
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