Combine arugula, walnuts, cheese, lemon juice, garlic and kosher salt in the food processor. Turn processor on.
With the processor, running slowly drizzle in the olive oil. Process until smooth, about 1 minute. Serve.
Notes
The lemon juice should help prevent the pesto from oxidizing. You can also store it with a layer of plastic wrap pressed on the top. Nutrition information for estimation purposes only.