In a blender or food processor, pulse the basil, pine nuts, garlic, 1/2 teaspoon of salt, and 1/4 teaspoon of pepper until finely chopped.
With the blender still running, gradually add enough oil to form a smooth and thick consistency.
Transfer the pesto to a medium bowl and stir in the cheese.
Season the pesto with more salt and pepper to taste.
Notes
The pesto will be thick. The trick is to slowly add pasta cooking water. The goal is to make this into the right consistency to coat the pasta without making it watery.