My husband thought you had to boil eggs for a half hour when we first got together, and he wondered why his centers were always black, lol!!
Start with a pot of COLD water. Put your eggs in. Water should just cover the eggs. Bring the pot to a boil, shut off the heat, and cover your pot (with the water in it) for 10 minutes!
Voila! Hard boiled, mostly unbroken eggs. There may be one, you can't ever tell! Run cool water on them to cool if you want to use them right away.
Let me know how it turns out!