Combine the basil, pine nuts, garlic and parmesan in a food processor or blender and pulse until chopped. Add the oil and puree until smooth. Salt and pepper to taste. Add more olive oil, as needed.
Store in the fridge for up to 1 week in an airtight container or jar. You can also freeze pesto. I like to pour it into an ice cube tray and freeze. Then add the frozen pesto cubes to a ziploc bag and store in freezer for up to 3 months.