Add the basil leaves, parmesan cheese, walnuts, garlic, kosher salt, and black pepper to the bowl of a food processor. Pulse a few times until all of the ingredients are coarsely chopped, scraping down the sides as necessary. Then, with the food processor on low speed, slowly drizzle in the olive oil until the pesto sauce is creamy and emulsified. Set aside.
2 cups basil leaves, ½ cup parmesan cheese, ¼ cup walnuts, 2 cloves garlic, ¼ teaspoon kosher salt, ¼ teaspoon black pepper, ½ cup extra virgin olive oil