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.