In a small saucepan, add the water, soy sauce, sugar, mirin, garlic, and ginger. Bring to a boil over medium-high heat, then reduce to medium-low and simmer for 3 to 5 minutes until sugar dissolves and marinade reduces slightly.

Fit a medium saucepan with a steamer basket, fill with water to reach the bottom of the basket, cover, and bring to a boil. Add eggs in a single layer and steam for 6 to 7 minutes for desired yolk consistency.

If no steamer, boil enough water to fully submerge the eggs and cook for 7 minutes.

Make an ice bath with ice and cold water in a medium bowl. Transfer cooked eggs to the ice bath immediately to fully cool.

Tap each egg with the back of a spoon to crack the shell and peel starting at the wide bottom end, rinsing in the ice bath to remove any stuck-on shells.

Add peeled eggs to the marinade, cover, and refrigerate for at least 4 hours and up to 24 hours. Store leftovers in a container with a tight-fitting lid.