Bring a large pot of well-salted water to a boil. Set up a bowl of well-salted ice water. Place the trimmed asparagus in the boiling water and let the water come back to a rolling boil. Remove asparagus from the boiling water and plunge immediately into the ice water. Remove from the ice water, pat dry, and reserve.
In a small bowl combine the olive oil, red wine vinegar, and Parmigiano-Reggiano. Season with salt. Toss the asparagus in the vinaigrette. Arrange on a serving plate and sprinkle with the crumbled egg white and yellow.