Boil 500 grams of pasta in a large pot of salted water until al dente. Drain and set aside.
In a blender or food processor, combine 1 cup of fresh or frozen green peas (thawed if frozen), 1/2 cup of fresh basil leaves, 1/4 cup of grated Parmesan cheese, 2 cloves of garlic, 1/4 cup of pine nuts, and salt to taste. Blend until smooth.
While the blender is running, slowly drizzle in 1/4 cup of olive oil until the pesto reaches a creamy consistency.
In a large pan, heat 1 tablespoon of olive oil over medium heat. Add the cooked pasta and green pea pesto sauce, tossing to coat the pasta evenly.
Cook for 2-3 minutes until the pasta is heated through and the sauce is well incorporated.
Serve hot, garnished with additional grated Parmesan cheese and fresh basil leaves.