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 of 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.