Toast pine nuts in a skillet, stirring constantly, until lightly browned. Transfer to a platter to cool. In a food processor, puree basil leaves and garlic together. Add cheeses, pine nuts, salt and pepper, blend until well incorporated and a smooth paste is produced. With the processor still running, add oil in a steady, thin stream until all the oil is added. Adjust salt and pepper, to taste.
Notes
Store any remaining sauce in a small jar and top with a small amount of olive oil to cover and keep basil from turning dark. Enjoy within one week, or freeze in ice cube trays to add to other sauces, as needed. (Ice cube tray slots are about a tablespoon in each slot making it easy to use small amounts, as needed. Once frozen, remove from the ice cube tray and store in a freezer bag until ready to use.)