Bring water to a boil in the saucepan. Water should be enough to cover the eggs (1 inch above the eggs).
Submerge the eggs carefully, preventing them from cracking. Reduce the heat to maintain a simmer/gentle boil, and cook the eggs for exactly 7 minutes.
After 7 minutes, immediately take out the eggs and soak in an ice bath for 3 minutes. Then, peel the eggs gently.
Mix soy sauce, mirin and water in a resealable plastic bag, to make the marinate. Submerge the eggs in the marinade in the sauce bag. Let it marinate overnight, or for an hour or two if in a rush.