Wash and dry the fresh basil. I spin mine in a salad spinner and then dab it dry with a paper towel. Pluck the leaves off the stems and place the leaves in a food processor or blender.
Heat a small skillet over medium heat. Add pine nuts and cook for 1 to 2 minutes stirring frequently until starting to brown. Watch them carefully so they don't burn. This brings out the aroma and flavor of the pine nuts. Allow to cool slightly, then add to food processor or blender.
Add the shredded parmesan cheese, garlic cloves, and sea salt.
Place the lid on and run the machine pouring olive oil into the section of the lid that can be removed while the machine is running. Mix thoroughly, stopping to scrape the sides if necessary.
Pour pesto into a jar and cover with a thin layer of olive oil to keep the herbs fresh for 2 to 3 weeks in the refrigerator. Seal jar with a lid before storing in the refrigerator.
Alternately freeze pesto in an ice cube tray and then place frozen cubes in an airtight freezer bag for 3 to 6 months. (You may consider leaving the cheese out until ready to use the pesto if you are freezing it, because some say that freezing the pesto with the cheese inside changes the flavor. If you choose to wait to add the cheese, I would use fresh grated parmesan instead of shredded parmesan, so you don't have to blend it up again.)