Potato and Green Bean Salad

For the vegetables: If your potatoes are of various sizes, cut them into roughly equivalent-sized pieces. Place the potatoes in a large pot of cold water with the salt. Bring to a boil over high heat, then lower the heat to maintain a vigorous simmer. When the potatoes are fork-tender, 10 to 15 minutes (depending on size), transfer them to a bowl with a slotted spoon. Add the green beans to the water and boil for 2 1/2 minutes. Transfer the green beans to a separate bowl. Rinse both vegetables in cold water until cool; drain well. Set aside.
For the arugula pesto: Combine the arugula, mint, olive oil, garlic, salt, and cheese in a mini food processor. Process until the mixture forms a fairly smooth paste with some texture left. Alternatively, you can use an immersion blender, or a regular blender if you make a double batch. Taste and adjust the seasoning.
To complete the salad: Toss the potatoes and green beans with the arugula pesto, several grinds of black pepper, and the walnut pieces, if using. Taste, add more salt if needed, and serve.