Turn on a food processor fitted with the steel blade, and drop in the garlic cloves. When they are chopped and adhering to the sides, stop the machine, scrape down the sides of the bowl and add the walnuts. Turn on the machine, and process until they are finely ground. Scrape down the bowl again, and add the arugula and the salt.
Pulse until the arugula is finely chopped, then turn on the machine and run while you slowly drizzle in the olive oil. When the mixture is smooth, stop the machine, scrape down the sides and process for another 30 seconds or so. Scrape out into the bowl of a mortar and pestle. Grind the mixture with the pestle for a smoother texture. Work in the cheese and combine well.