Cut the avocado into half and discard the seed. Take out the flesh using a spoon and add it to the medium size blender jar. Discard the skin.
Add basil leaves, walnuts, garlic, olive oil, salt, black pepper, and parmesan cheese to the blender jar.
Blend to make a slightly coarse paste. Scrap the sides of the jar once while blending. Transfer the pesto to an airtight container and drizzle a layer of olive oil to prevent it from turning black from oxidation. Secure the lid and refrigerate.