Toast the walnuts over medium heat for 3-4 minutes until warm and fragrant. Remove from the heat and transfer to a plate to cool completely.

While the walnuts are cooling, add the garlic to the bowl of a food processor and blend for 10 seconds to break up the garlic.

When the walnuts are cool, add them to the food processor and blend again until they're broken down into very small pieces, 1-2 minutes.

Add the rest of the ingredients, except the avocado oil and water, and blend on high for 1-2 minutes until the arugula is broken down. Scrape down the sides of the food processor as needed.

With the food processor on medium speed, slowly drizzle in the avocado oil until the pesto becomes much thinner and starts to look like pesto.

If it's too thick, add water one tablespoon at a time to thin it out to your desired consistency.