Combine the basil, Parmesan, pine nuts, and garlic in a food processor and pulse until finely chopped. With the machine running, pour in a thin, steady stream of the oil, blending until the mixture is well combined and emulsified. Store in the refrigerator in an airtight container covered with a thin layer of oil (to preserve the color) for up to 1 week. Sprinkle with additional Parmesan (and basil leaves, if you wish) just before serving. (This can be made 2 to 3 days in advance and kept in the freezer for up to 2 months.) Note: To make this recipe even simpler, buy prepared pesto and spruce it up at home with chopped pine nuts and freshly grated Parmesan before serving.