When you have a lot of hard-cooked eggs to peel, the task can seem to take FOREVER: all those little bits of shell just love to cling to the eggs, and inevitably you end up marring your eggs with pockmarks as you pick away bits of shell. But this tip will have you on your way to deviled eggs in no time flat.
After cooking your eggs, drain off the water and leave the eggs right in their saucepan. Put the lid back on and give the pan a few firm shakes. When you remove the lid, you'll see the eggshells are webbed all over with tiny cracks (if they're not, put the lid back on and give it a few more shakes).
Now, you'll find the shells pull away from the eggs in great big chunks, plus they'll leave the eggs smoother without all those pockmarks. To speed things along even more, run water over the eggs, which will help the shell separate further.