Place all the ingredients except black pepper in your blender or food processor and pulse several times until you get a smooth mixture. You may need to scrape down the sides of the blender with a rubber spatula.
Taste and adjust for salt. Stir in some coarsely ground pepper if you'd like. Store in an airtight jar in the refrigerator. I like to pour over a couple teaspoons of olive oil to prevent the pesto from darkening.