Place the pesto ingredients (parsley, spinach, lemon juice, 1 Tablespoon toasted pine nuts, grated Parmesan cheese, smashed garlic and salt and pepper in the bowl of a food processor. Process the ingredients until they are smooth. With the food processor running, add the olive oil through the spout at the top of the food processor in a slow steady stream to the ingredients in the processor bowl. Process until the ingredients are smooth, about 1 minute.
Place the 4 cups of shredded rotisserie chicken, 2 cups cooked edamame, the drained and rinsed chickpeas ,1 cup chopped cucumber and 4 cups arugula in a large bowl. Add the pesto to the bowl and toss the ingredients to combine them.
To serve, divide the arugula between 4 plates, top the arugula with the chicken mixture. Top the salad with the remaining toasted toasted pine nuts. Serve immediately. Place any leftovers covered with plastic wrap in the refrigerator.