Bring a large pot of salted water to a rolling boil.
Add the potatoes to the water and boil for about 10 minutes until fork tender. Drain the water and place the potatoes in a large bowl in the fridge until cool enough to handle.
Meanwhile, add the arugula, nuts, garlic, parmesan, lemon juice, pepper flakes, salt, and pepper to the bowl of your food process or high powered blender.
Pulse 4-5 times until the mixture is coarse. Turn the food processor on low, stream in the olive oil until the pesto is smooth.
Once the potatoes have cooled, cut them into halves or fourths as desired.
Pour the pesto over the potatoes and stir to coat. Serve immediately for a warm potato salad, or chill until ready to serve.
Potato salad is good in the refrigerator for up to 3 days.