Put basil, garlic, and pine nuts on a cutting board. With a mezzaluna or sharp knife, finely chop the ingredients and add to a jar. Add the Parmigiano cheese, salt, and 1/2 cup olive oil and mix all the ingredients well. Top up with the remaining extra-virgin olive oil. Cook's Note: Pesto can be served fresh or it can be preserved in the refrigerator or freezer in an air-tight container. If freezing, omit the cheese and drizzle the top with oil. Thaw, then stir in the cheese.