Cover garlic in a small saucepan with water by 1 inch. Bring to a boil over high heat, then immediately drain and let garlic cool to room temperature.
In a blender or food processor, pulse basil, garlic, pine nuts, and the cheese to incorporate. Pour in the oil in a slow steady stream, and pulse until combined; season with salt. Serve immediately or cover with a layer of oil and store in an airtight container in the refrigerator for up to 3 days or freeze in small amounts for easy use.