Pulse basil, pine nuts, garlic, salt, and pepper in a food processor until finely chopped.

With the motor running, slowly pour olive oil into the feed tube and process until a thick paste forms, scraping the sides as needed.

Transfer the mixture to a medium bowl and stir in the Parmigiano-Reggiano.

Season to taste with more salt and pepper.

To store in the refrigerator, transfer pesto to an airtight container, cover with a thin layer of olive oil, and refrigerate for up to 1 week.

To freeze, portion the pesto into small plastic freezer bags or ice cube trays and freeze until solid.

If using ice cube trays, transfer the cubes to a plastic freezer bag for storage. Defrost overnight in the refrigerator.