In a large, deep skillet, add enough salted water to reach a depth of 2 inches; bring to a boil. Add the asparagus and cook until crisp-tender, about 3 minutes. Transfer to a bowl of ice water and let stand until chilled. Drain and pat dry.
In a small bowl, whisk together the apple cider vinegar, shallot, mustard, tarragon and orange peel. Slowly whisk in the olive oil until combined; season with salt and pepper.
Cut the hard-boiled eggs in half, then press through a sieve into a small bowl. Toss the asparagus with some of the vinaigrette. To serve, drizzle with more dressing and top with the eggs.