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1
Combine the soy sauce, mirin, and sake in a small saucepan and bring to a brief simmer to cook off the raw alcohol. Remove from the heat and allow to cool completely. The marinade is ready when it smells cooked and integrated rather than sharp with raw sake.
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2
Bring a pot of water to a full, rolling boil. Lower the eggs one at a time into the water on a spoon — do not drop them. The moment the last egg enters the water, start the timer. Cook for exactly 7 minutes. At 6 minutes the yolk centre remains translucent and very loose; at 8 minutes the yolk begins to set fully. The dish lives or dies at this step: a deviation of one minute in either direction eliminates the jammy, orange-toned, semi-solid yolk that defines the egg's role in the bowl.
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3
Transfer the eggs immediately into an ice-water bath. The shock halts cooking at the moment the timer ends; eggs left in hot water, even off the heat, continue to cook. Leave in the ice bath until the eggs are cold to the touch throughout, approximately 5 minutes.
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4
Peel the eggs under cold running water. The running water separates the membrane from the white, producing a clean, unbroken surface. The peeled whites should be smooth and fully set, with no translucent patches.
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5
Place the peeled eggs in the cooled marinade in a container or zip-lock bag, ensuring the eggs are fully submerged or, if in a bag, in maximum contact with the liquid. Marinate for a minimum of 4 hours and a maximum of 3 days under refrigeration. Longer marination deepens flavour but risks over-salting; at the minimum time the marinade should be perceptibly present on the white without overwhelming it.