To make the Pesto, put the pine nuts and garlic in the food processor and pulse. Add the basil and pulse, adding the oil gradually, until all ingredients are combined to a nice, creamy consistency. Add the cheese at the end and a little more oil if required.
Bring a large pan of salted water to the boil. Add the potatoes and pasta and cook for a couple of minutes, until the pasta is soft and silky. As long as the potato slices are thin enough, they should be cooked in this time too.
Place half of the pesto in a serving bowl with a couple of tablespoons of the pasta cooking water. Toss in the pasta, potatoes and beans and stir to combine. Add more pesto until it is the consistency you like and finish with extra cheese and a drizzle of oil, to taste.