Mix together the water, soy sauce, mirin, and sugar in a saucepan. Boil for a few seconds and mix well. If desired, add katsuobushi, then remove from heat and let cool to room temperature.

In a different saucepan, boil water with vinegar, then add the eggs straight from the fridge. Cook them for 6 minutes and 30 seconds.

Immediately dip the eggs into a bowl of ice water to stop the cooking process. Let them cool, then peel them carefully.

In a suitable container, add the peeled eggs. Pour the marinade over the eggs, ensuring they are completely covered.

Add a paper towel on top to guarantee all sides of the eggs absorb the marinade. Alternatively, use Ziploc bags to marinate the eggs.

Marinate in the refrigerator for 12-24 hours, depending on the desired flavor intensity. Store in an airtight container.