Toast your walnuts in a dry skillet over medium low heat until they just start to turn golden brown - about 7 minutes, tossing frequently
Place basil, garlic, walnuts, parmesan cheese, and salt in a food processor
Process until fully combine
With the food processor running, slowly stream in olive oil - you may need to stop the food processor and scraps down the sides to be sure all the ingredients are mixed in
Once all of the oil is added, keep the food processor running until a smooth pesto remains
Place in an airtight container and store in the fridge for up to one week
Notes
Use pecorino romano instead of parmesan if you like it better
Feel free to use almonds or pecans in place of walnuts
Pour a thin layer of olive oil over top of the pesto in the jar to prevent oxidation