Bring water to a boil in a large pot. Carefully lower eggs into pot and continue to boil for 30 seconds. Cover tightly, reduce heat to low (water should maintain a bare simmer), and continue cooking for 11 minutes. Serve immediately if serving hot. If serving cold, immediately place eggs in a bowl of ice water and allow to cool for at least 15 minutes before peeling under cool running water.
Hard boiled eggs with the shell still on can be stored in the refrigerator for up to 5 days; with the shell removed, they can be refrigerated for up to 1 day. To peel, first gently tap hard-boiled eggs all over to thoroughly crack the shell, then remove shell under a thin stream of running water (the water helps get under the shell and lift it off the egg).
source: https://www.seriouseats.com/recipes/2009/10/print/perfect-boiled-eggs-recipe.html