Steam asparagus until tender , 3-5 minutes.
Transfer to a bowl of ice water to stop cooking.
Drain well and pat dry with paper towels.
Whisk together vinegar, shallot, mustard, salt and pepper in a small bowl and add oil in a slow stream whisking until emulsified.
Whisk in tarragon.
Toss asparagus with 1 Tbs of vinaigrette.
Spoon remaining dressing over asparagus and top with the egg.
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