Bring a large pot of salted water to a boil for the pasta. Combine the basil, pine nuts, garlic, and olive oil in a blender and blend to a puree. Add the cheese, salt and pepper, and blend again.
Cook the pasta in the boiling, salted water until al dente, about 3 minutes. Drain and transfer to a large bowl. Add the pesto and toss. Taste for salt and pepper, and add a drizzle of oil, top with Parmesan shavings and torn basil.
Leaves from 2 bunch fresh basil
2 tablespoons pine nuts, untoasted
1 garlic clove
1/2 cup extra-virgin olive oil
1/2 cup freshly grated Parmigiano-Reggiano
Salt and freshly ground black pepper
1 pound angel hair pasta