Preheat oven to 350 degrees F. On a baking sheet, spread the pine nuts and bake for about 5 minutes, then stir. Continue baking until the nuts are golden brown and highly aromatic, stirring occasionally.
After the nuts cool completely, chop them finely.
Fill a medium-sized saucepan halfway with water, place over medium heat and bring to a boil. Next to the pot, fill a large bowl with ice and water. Dip a few of the basil leaves into the boiling water with tongs, blanch for 3 seconds, then remove them from the water and place them in the ice water. Repeat until all of the basil has been blanched, adding ice to the water as necessary.
Drain the basil in a colander and with a towel, pat dry.
In a food processor or blender, mix the basil, cheese, pine nuts, salt, garlic, pepper, and all but 1 tbs. of the olive oil. Process until the pesto is smooth and uniform.
Pour the pesto into an airtight container, adding the remaining olive oil to the top as a protective layer. Pesto can be stored in the refrigerator for up to 5 days.