Put the tangerine juice in a small non-reactive saucepan and bring to a boil. Cook until reduced to 1/2 cup. Let cool to room temperature.
Peel the tangerines, removing all the white pith, and segment over a bowl to catch both the segments and the juices. Cover and refrigerate until very cold.
Combine the reduced juice, tarragon, egg yolk, and salt and pepper, to taste, in a blender and blend until well mixed. With the machine running, add the 1 cup olive oil, at first by drops and then, as mixture emulsifies, in a thin, steady stream until all the oil is incorporated. Taste, for seasoning. Scrape into a jar, cover, and refrigerate until needed. You should have about 1 2/3 cups mayonnaise. Keeps 2 to 3 days, refrigerated.
Prepare the grill and let burn down to medium coals. Toss the cooled asparagus with about 1 tablespoon olive oil and season with salt and pepper. Grill over medium to low coals, turning the spears as needed, until they take on a little color and are just tender, about 6 minutes. Cover the grill, if necessary, to maintain the heat.
Arrange the asparagus on a platter with the reserved tangerine segments. Dot with the mayonnaise, and drizzle with any tangerine juice left in the bowl. Garnish with fresh or candied zest and the nuts, if using. Serve at once.
Cook's Note: Every cook has insecurities. One of mine is mayonnaise. I always get a little anxious until I see it coming together in the blender. If the mayonnaise is too thick, thin it, with the machine running, by pulsing in a little cool water. If you are concerned about raw eggs, use a pasteurized egg product or an egg substitute such as Egg Beaters.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.