Cook the asparagus in a wide pot filled with boiling water for 2 to 3 minutes, or until just tender. Drain asparagus, cool in ice-cold water, and then drained well again. Arrange asparagus in neat rows on a serving platter.
Cut the egg in half and pull out the yolk. Finely chop the yolk and set in a small bowl. Now finely chop the white and set in a second small bowl.
Make dressing by combining remaining ingredients in a third small bowl. (Chopped egg, asparagus and dressing can be made several hours before needed. Keep all covered and refrigerated until ready to serve.)
To serve, spoon the dressing over the asparagus. Neatly sprinkle the asparagus with chopped egg yolk, and chopped egg white, and serve.
Recipe Options: Instead of dried tarragon, use 1 Tbsp. of fresh tarragon in the dressing. If you prefer its coarser texture, instead of regular smooth Dijon mustard, use whole grain - also called "old-style" - Dijon mustard in the dressing for the asparagus. If you can't or don't wish to have egg on the asparagus, simply omit and call your creation asparagus with vinaigrette dressing.