Tip: click step to get into cook mode
Toast the walnuts in a small skillet over medium heat until fragrant and the oils just begin to release, about 5 minutes. Remove from the heat and cool completely.
When the walnuts have cooled, transfer to the bowl of a food processor along with the arugula, Parmesan, lemon juice and garlic. Turn on the machine and, with the motor running, slowly add the olive oil. When the pesto is slightly smooth, season with salt and pepper. (There will be a scant 2 cups.)