Here's a great new method of cooking eggs by Chef John (video below).
You actually steam them in a small amount of water in a covered pot.
It is quicker because there is less water to get boiling.
I use this method every time now. I will never make a hard boiled egg any other way, it works that good.
I steam for about 10 minutes so they are not as soft in the middle.
 
https://youtu.be/GPFHv5SKbZ4