For eggs that peel easily and cleanly, we've found no better method than this one, from chef Ryan Pollnow of Aatxe ("Ah-chay") restaurant in San Francisco.
Makes 12 eggs
1. Bring 4 qts. water to a boil in a large pot and add the salt. Pierce eggs with a clean thumbtack (this lets the egg's air pocket expand without cracking the egg). Lower eggs carefully into boiling water, bring to a simmer, uncovered, and simmer 6 minutes. A small thread of white will escape from the shells; this is normal and won't affect the final result.
2. Remove pot from the heat and let sit, uncovered, 6 minutes.
3. Transfer eggs to a bowl of ice and cold water; let sit 6 minutes. Crack gently all over. Peel eggs.