When I was on a film set, someone asked me how to peel eggs easily. I admit, I often found that I was taking more of the egg off trying to get the shell. I did a lot of research and finally found a way to peel eggs easily.
First, start your water on high and bring to a boil. Next, when the water is boiling, with a big spoon slowly lower the eggs in the water. Be careful not to burn yourself: cover and lower heat to simmer. Simmer the eggs for 13.5 minutes for hard-boiled eggs. Carefully empty water and put the eggs in an ice-water bath. Once cooled down, crack the shell on both ends of the egg and lightly role to break the shell. Lift shell on the end of the egg that has like an air pocket. And voila nicely smooth peeled eggs.