In a medium saucepan combine the eggs and salt and bring to a boil.
Remove from heat, cover and allow to sit undisturbed for 13 minutes.
Remove eggs from saucepan and immerse in an ice water bath to stop the cooking process.
In a medium saucepan over high heat, bring all remaining ingredients to a boil over high heat.
Turn the heat to the lowest setting that will still maintain a gentle simmer, and simmer for 45 minutes or until reduced by about half.
Meanwhile, crack the hard-boiled eggs all around by tapping with a soup spoon and/or gently rolling the eggs on a countertop. You want an even, cracked pattern around each egg, but you don’t want large bits of shell falling off each egg.
Place the prepared eggs in a deep bowl big enough to hold them, hold a strainer over the bowl and the prepared eggs, and strain the hot tea infusion into the bowl to cover the eggs.
Weigh down the eggs with a small plate or bowl and store in the refrigerator for 24 hours to allow the tea infusion to flavor the eggs.
Peel the eggs and serve. Covered, these will keep in the refrigerator for several days.