Put all 6 eggs in a pot and cover with water about 1 inch above the eggs. Add 1 teaspoon of salt. Heat and let boil for 2 minutes, then remove from stove. The salt will help the eggs crack easier.
Remove eggs from boiling water using a slotted spoon, and place eggs in a bowl of cold water. Let cool 3 minutes.
While eggs cool, add the rest of the ingredients to the hot water you were boiling eggs in. Stir and set aside.
After eggs are cool enough to touch (about 3 minutes in the cold water), pick up an egg and hit it with the back of a spoon to crack the shell. Small pieces of flaked shell may fly off, that is okay.
Repeat with the remainder of the eggs. Set eggs in the water with sauce after you finish tapping each one.
Heat the pot of eggs and sauce on medium heat to bring to a boil, then reduce to a simmer (low heat) and simmer for 3 hours to let the flavor soak in through the cracks in the shell.
Let eggs chill in the fridge overnight, sitting in the sauce they simmered in.
Peel eggs and serve the next day!