Pulse basil leaves, cheese, pine nuts, and garlic in a food processor until finely chopped. With the machine running, pour in olive oil in a thin, steady stream, blending until the mixture is well combined and emulsified. Serve pesto with a long, thin pasta such as fettuccine or spaghetti. Store in an airtight container covered with a thin layer of oil (to preserve color) in the refrigerator for up to 1 week.