Steam asparagus on a steamer rack set over boiling water, covered, until just tender, 3 to 5 minutes (depending on thickness), then 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.
Halve egg and force each half through a coarse sieve into a bowl. Toss asparagus with 1 tablespoon vinaigrette and divide among 4 plates. Spoon remaining dressing over asparagus and top with egg.
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