Prepare a bowl of ice and cold water. Put asparagus in a 12-inch heavy skillet, then cover with cold water. Bring water to a boil and add 2 teaspoons salt, then reduce heat and simmer asparagus, uncovered, until just tender, 6 to 8 minutes. Transfer with tongs to ice water, then to a clean kitchen towel. Pat dry. Whisk together vinegar, shallot, mustard, pepper, and remaining 1/4 teaspoon salt in a small bowl, then add oil in a slow stream, whisking until emulsified. Halve eggs, then force through a medium-mesh sieve into another small bowl. Toss asparagus with 1 tablespoon vinaigrette in a large shallow bowl, then divide asparagus among 4 plates. Spoon additional vinaigrette over asparagus and top with egg.