Cook the pasta according to instructions until al dente, probably about 10 minutes.
Put half the spinach, olive oil, lemon zest and juice, garlic cloves, toasted walnuts, half the parmesan, basil leaves into a food processor. Blitz until it forms a rough paste and add salt and pepper as appropriate.
Once the pasta is done drain but reserve a splash of the cooking water. Mix the pesto through the pasta along with the chopped spinach. Serve and garnish with the remaining parmesan.