Using the metal blade of your food processor, grind the walnuts until they are a fine meal.
Add the parsley, garlic, lemon juice and lemon zest and pulse until coarsely chopped.
Drizzle in the olive oil with the motor running until pesto is even chopped and to the texture you want.
Stir in salt and taste and adjust seasoning.
Notes
To store in the fridge, place in a lidded jar and cover with a layer of olive oil. It will keep for about 2 weeks. It will keep in the freezer for about 6 months and then it might lose some of it's fresh flavor. I like to freeze mine in ice cube trays and then store the cubes in a vacuum sealed bag.