Prepare the potatoes according to package directions. You can microwave, oven roast, or air fry, all of which I’ve tested & work great for this recipe! Once prepared & cool enough to handle, halve any larger potatoes into bite-sized pieces.
Place basil, parsley, chives, lemon zest & juice, garlic, walnuts, pine nuts, & cheese (if using) a food processor. Season with S&P as desired. Pulse until mixture is roughly chopped & combined. With food processor running, slowly stream in olive oil. Process until combined, stopping to scrape down the sides as needed, until the pesto as rustic or creamy as desired. Taste and season with additional S&P as desired. Set aside.
Add prepared baby potatoes & arugula to a large mixing bowl. Pour the green goddess pesto over top. Toss to combine, seasoning with additional S&P as desired. Serve immediately, garnished with fresh herbs, grated cheese (if using), & crushed red pepper flakes, as desired.