Preheat oven to 350˚F.
Toast walnuts on a cookie sheet for 7-10 minutes; allow to cool.

Put arugula leaves in a food processor with peeled garlic. Process until smooth, scraping down the insides of bowl once or twice. Add walnuts and process until smooth. With machine running, add olive oil in a slow stream. Transfer mixture to a bowl and stir in cheese by hand.
Season to taste with salt and pepper.