Begin by cooking the fusilli: Bring the water to a boil in a large pot. Add the kosher salt and the fusilli.
While the fusilli cooks, make the Basil and Walnut Pesto: Heat a small skillet on low heat, and cook the walnuts until toasted about five minutes.
Put the walnuts in a food processor, and process until finely chopped. Add the rest of the ingredients, except for the pasta water, and process until everything is minced and combined. Add the pasta water, and process until a creamy sauce is formed.
Drain the fusilli, and pour it into a large bowl. Add the pesto and stir until combined. Serve with extra Parmesan cheese.