In a large pot of boiling salted water, cook the green beans and potatoes then remove them to a bowl with a slotted spoon. In the same pot, cook the pasta until al dente (according to package instructions). Reserve 125 ml of the cooking water, drain and return the pasta to the pot.
Meanwhile, prepare the pesto. Using a small food processor pulse together the pesto ingredients until smooth. Season with salt and pepper, to taste.
Add the pesto, green beans and potatoes to the pot with the pasta. Add a little of the reserved cooking water and toss to combine. Serve in bowls and garnish with nutritional yeast.