1 cup water
1 cup sake
½ cup soy sauce
½ cup mirin
½ cup sugar
6 large eggs
Combine water, sake, soy, mirin, and sugar in a medium bowl and whisk until sugar is dissolved. Set aside.
Place the eggs in a medium pot and add water to 2 inches over eggs. Bring to a boil, reduce to a simmer and cook for exactly 6 ½ minutes. Remove and place into ice water to stop the cooking.
Carefully peel eggs under cold running water (the whites will be quite delicate).
Transfer eggs to a bowl that just barely fits them all. Pour marinade on top until eggs are covered or just floating. Place a double-layer of paper towels on top and press down until completely saturated in liquid to help keep eggs submerged and marinating evenly. Refrigerate and marinate at least four hours and up to 12. Discard marinade after 12 hours. Reheat in ramen soup to serve.