It's true that older eggs are easier to peel when they've been hardboiled. It's also true that you don't have to wait for your eggs to get old to remove the peels without destroying the eggs.
I use Julia Child's method of alternately heating and chilling the eggs. Here's how it works.
For a dozen eggs, choose the best you can find, preferably pasture-raised eggs. Place them at the bottom of a large, heavy pot and cover with 3 1/2 quarts cold water. Bring the pot to a boil. As soon as it begins to boil, remove the pot and allow the eggs to sit, covered, for exactly 17 minutes.
When the 17 minutes have elapsed, carefully remove the eggs to a large bowl of iced water (you may want to buy a bag of ice for this). Allow the eggs to sit in the iced water for 2 minutes. Meanwhile, put the pot on the stove and bring the water back to a boil. (Remove the eggs from the iced water after the 2 minutes are up.) In batches of 6, return the eggs to the boiling water for 10 seconds only. Then remove again and place back in the iced water. Crack each egg in several places (or not, if you are planning to decorate them for Easter) and let the eggs rest in the iced water until well chilled.
Your eggs are now ready for peeling.