This post has been updated. See new info below…
To make the prefect hard-boiled egg each time, you actually do not boil it. You bake it.
Cooking instructions: Put the eggs in a muffin tin and bake for 25 min. at 325. Take the eggs out and put into a bowl of ice water until cooled. The perfect egg.
After doing this several times, I noticed a small brown dot on the eggs where they touched the pan. Not really a big deal as you can just pinch the brown dot off however to get rid of the small burn mark, just use a silicone muffin pan or muffin cups, like this:
Props to Alaskafromscratch and Me!