Spread the pine nuts on a rimmed baking sheet; toast in the oven until golden and fragrant, stirring once, 5 to 8 minutes (watch closely, so they don't burn!) Transfer the toasted pine nuts from the baking sheet to a paper towel to prevent further browning and let them cool completely.
In a food processor, combine the pine nuts, basil, cheese, and garlic; season with salt and pepper. Process until finely chopped. With the machine running, pour the oil in a steady stream through the feed tube, and continue processing until smooth. Store in a covered container in the refrigerator for up to one week.