Blanch the basil leaves in a large pot of boiling water for 30 seconds, then transfer them to a bowl of ice water to stop the cooking. I like to use a fine-mesh strainer to place the basil in the water so it's easy to transfer it to the ice bath.
Combine all the ingredients in a high-powered blender or food processor and mix until well combined. Taste and adjust the salt as needed. If you skip the parmesan cheese, the pesto may need a little more salt.
Store in the fridge and use within a few days, or store in the freezer for several months.