Boiling Eggs for Deviled Eggs
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Choosing Eggs - For hard-cooked eggs, it's best to use older eggs, like two
weeks old or more. Why? Older eggs shell more cleanly.

Cooking the Eggs - Hard-boiled eggs are easy and quick to prepare. Eggs in
the shell should be cooked over high heat just until the water begins to
boil then removed and left to stand until done. Never leave your eggs to
boil! If eggs are boiled for any length of time, the yolks will become hard
or may turn an unattractive greenish-gray. The process to full-proof
hard-boiled eggs is an easy one. Simply put the eggs in a pan roomy enough
to hold them without crowding, with cold water to cover by at least one
inch. Next, over high heat, heat the water and eggs until just fully
boiling. Once a full boil is achieved, remove the saucepan from the heat,
cover tightly and let them stand for 15 minutes. After the time has
elapsed, pour off the hot water and run cold water over the eggs to achieve
a faster cooling. I let the cold water run over the eggs for ten minutes
and add some ice to get them cold fast. This not only stops the cooking
process, but it also makes it easier to peel the eggs. Then I put them in
the refrigerator for an hour before making the recipe.

Shelling Hard-Cooked Eggs - Using older eggs make this job a lot easier.
But you can get away with using fresh eggs if you follow my method. First,
you want to crack the shells. The easiest way to do this is to place all
the eggs in a roomy saucepan again and shake them around. The agitation
will break up the shells nicely. Then, to remove the shells, run each egg
under cold water and begin to peel off pieces of the shell. I always start
at the large end, but it really doesn't make a difference.

From: Deviled Eggs Recipe.org