Boil the pasta according to packaging instructions then drain.
Blanche the peas in boiling water for 2 minutes, rinse with cold water, then drain - but set aside 1 cup of the the cooking water.
Grate the cheese into a blender, add garlic (minced), add the basil leaves, lemon juice and half of the oil, then blend to a coarse paste.
Mix the pesto with the peas, squeeze it with a fork for a few seconds. Season with salt and pepper.
Put the spaghetti back in the pan, add 3 tablespoons of the cooking water. Heat through, then add the remaining oil and toss with the pea pesto.
Serve with a little lemon juice squeezed over it and garnished with chopped basil leaves.