Cut the avocado in half and discard the seed. Take out the flesh using a spoon and add it to a medium-sized blender jar. Discard the skin.
Add basil leaves, walnuts, garlic, olive oil, salt, black pepper, and parmesan cheese to a food processor or a 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 over it to prevent it from turning black from oxidation. Secure the lid and refrigerate. Use as required.
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Notes
To make a vegan avocado pesto, replace Parmesan cheese with nutritional yeast.You can also add lemon juice and zest for a tangy kick to the pesto.I suggest grating the Parmesan cheese freshly for use in this recipe. If not, then use finely grated cheese. Avoid using shredded cheese from a bag, as it may contain anti-caking agents such as cellulose, which can make the pesto gritty.