For this recipe, start with raw asparagus and let the smoke transform it. What grilling does for most foods, it does in spades for spears of asparagus. To make the job even easier, use a grill basket, which will give you more control.
Light grill or heat oven broiler. In a small bowl, whisk together the oil, salt, and 1 tablespoon of the tarragon. Pour over the asparagus and set aside.
In another small bowl, combine the mayonnaise, orange juice and peel, cayenne, and remaining 1 tablespoon of tarragon and anise seed if using; set aside.
Arrange the asparagus in a single layer in a grill rack, or carefully arrange the spears on a grill perpendicular to the grill grate. (If broiling, arrange on a baking sheet in a single layer.) Grill about 7 minutes over medium heat or until tender, turning once after 3 minutes. Or broil 4 inches from the heat source for 5 minutes, turning once. Remove the asparagus to a platter and serve with the orange mayonnaise.