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 ripe avocado (peeled and pitted), 1 cup fresh basil leaves, 2 cloves of garlic, 1/4 cup pine nuts, 1/4 cup grated Parmesan cheese, 1/4 cup olive oil, juice of 1 lemon, salt, and pepper to taste. Blend until smooth and creamy.
In a large mixing bowl, toss the cooked pasta with the avocado pesto sauce until well coated.
Serve the avocado pesto pasta immediately, garnished with extra Parmesan cheese, fresh basil leaves, and a drizzle of olive oil.