Prepare an ice water bath in a large bowl, and bring a large pot of water to a boil. Put the arugula in a large sieve and plunge it into the boiling water. Immediately immerse all the arugula and stir so that it blanches evenly. Blanch for about 15 seconds. Remove, shake off the excess water, then plunge the arugula into the ice water bath and stir again so it cools as fast as possible. Drain well.
Squeeze the water out of the arugula with your hands until very dry. Roughly chop the arugula and put in a blender. Add the garlic, salt and pepper to taste, olive oil, 2 tablespoons of the pine nuts, and the vitamin C, if using. Blend for at least 30 seconds. In this way the green of the arugula will thoroughly color the oil. Add the cheese and pulse to combine. The pesto will keep several days in a tightly sealed container in the refrigerator.
Pull out before dinner to get to room temperature. Before serving, add the remaining 1 tablespoon toasted pinenuts.