Cook the pasta in a large pot of well-salted boiling water according to package directions. Before draining the pasta, reserve about ¾ cup of the starchy pasta cooking water. Drain.
Make the Pesto Sauce
While you're waiting for the pasta water to boil and waiting for the pasta to cook, prepare the pesto sauce. Place the Parmesan, pine nuts, garlic, and salt in a food processor. Pulse to combine.
Add the basil to the food processor, and slowly drizzle in the olive oil while pulsing. Process until the sauce comes together in a uniform, creamy consistency, scraping down the sides occasionally and adding extra olive oil, if necessary.
Taste and season with additional salt and black pepper, if desired.
Toss the Pasta with the Sauce
Place the hot cooked pasta in a large bowl. Gradually add the pesto sauce (you might not want all of it), about ¼ cup of the pasta water, and the butter (if using). Stir gently to combine, adding a little bit more pasta water, as necessary, until the sauce is silky and smooth. Taste and season with additional salt and pepper, if desired. Garnish with extra Parmesan cheese and serve.
Notes
This recipe yields enough sauce for about 1 lb. (or 1.5 lbs.) pasta. You can double the ingredients for a larger batch.If you have extra pesto, place in an airtight container with the smallest top surface area. Pack the pesto tightly to eliminate air pockets, and pour a thin layer of olive oil on top. Then press a piece of plastic wrap directly onto the oil before closing the lid. The homemade pesto will last in the refrigerator for up to 1 week or in the freezer for up to 6 months.