Put eggs (cook as many as you wish to use later) in cold water to cover in a medium saucepan. Bring to a boil, lower heat to medium low and cook for 12 minutes, or until hard boiled. Drain water from pan and refill pan with cold water. Drain water again, crack egg shells, and refill pan with cold water, allowing eggs to cool as quickly as possible.
Drain and peel eggs (you will only need one for this recipe). Shred the egg white and yolk. Either coarsely chop on side of boxed grater or use an egg slicer to thinly slice in one direction, turn 180 degrees and slice again.
Remove the tough lower ends of the asparagus stalks by bending until they snap off. Discard the ends.
Bring a large pot of water to a boil, put the spears in and cook for 3 minutes or until just tender.
If serving warm: Drain and dry off asparagus spears by blotting with a tea towel. Proceed to step 7.
If serving room temperature: Remove the spears from the boiling water and immerse in a bowl of iced water. Allow asparagus to cool and blot dry. Cover with plastic wrap until serving time.
Drizzle oil over asparagus and toss gently. Arrange on a plate and then sprinkle with capers, salt and pepper. Place grated egg on top along the middle of the stalks so that the tops and bottoms of the asparagus remain visible.