Snap off and discard tough ends of asparagus. In a 5- to 6-quart pan over high heat, bring 2 quarts water to a boil. Add asparagus; cook, uncovered, until barely tender when pierced, about 5 minutes. Drain and immerse in cold water. When cool, in about 5 minutes, drain.
Meanwhile, in a small bowl, mix oil, vinegar, mustard, and tarragon.
Arrange watercress and radicchio (whole leaves or slivered) on a platter. Top with asparagus. Drizzle dressing over asparagus and greens. Add salt and pepper to taste.