Combine basil, pine nuts, garlic, lemon juice, and salt in a food processor. Then slowly add in olive oil until completely processed. Then add the parmesan and mix.
Potato Salad
Add potatoes to a large pot and cover with cold water and 1 tablespoon salt. Bring to a boil and boil until fork tender, about 7 minutes of boiling.
Bring a smaller pot of water to a boil and add green beans and boil for 3-4 minutes. Remove and drain. Transfer green beans to a bowl of ice water.
Drain the potatoes and transfer them back to the hot pot so that the moisture continues to steam off for 3-5 minutes. Transfer the potatoes and green beans to a large bowl. Stir in red onion and arugula. Then add ⅓ cup of pesto and stir.
Cover potato salad and marinate at room temperature for 1 hour and then transfer to the refrigerator. This will help the flavors from the pesto penetrate the potatoes.
Notes
When making the pesto, you want it to be slightly looser than normal. I upped the oil from ¼ cup to ⅓ cup and the lemon juice from half a lemon to a whole lemon. Think closer to a vinaigrette but not quite.