Mix together the water, soy sauce, mirin, and sugar. Boil for a few seconds and mix well.

If desired, add katsuobushi, then remove from heat and let cool to room temperature.

Boil a saucepan of water with vinegar. Add eggs (straight from the fridge) and cook for 6 minutes and 30 seconds.

Dip eggs in a bowl of ice water to stop the cooking process. Let them cool, then peel.

In a suitable container, add the eggs. Pour the marinade over them, straining it as you go. Ensure the eggs are completely covered in marinade.

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

Marinate for 12-24 hours in the refrigerator. Store in an airtight container and consume within approximately 3 days.