Cooking the eggs: Bring the eggs to room temperature. In a pot of boiling water, cook the eggs for 12 minutes to make hard-boiled eggs and for 7 minutes 30 seconds for soft-boiled eggs. Whichever you like.
While the eggs are cooking, prepare the marinade. Put all ingredients for the marinade into a pot. Bring it to a boil, then let it cool off.
Peel the boiled eggs. Soak the eggs in the marinade.
If your eggs stick out from the marinade, soak a sheet of paper towel in the marinade and use it to cover the eggs.
Marinate the eggs for 1/2 to 1 day to serve. The pictured eggs are a little spotty. I'll do better next time.
You can also use mentsuyu to simplify things a bit. Adjust the consistency of the mentsuyu so that it's slightly stronger flavor, and use it to marinate the eggs.
Story Behind this Recipe
I made this because I wanted seasoned eggs as a topping for my ramen. I made mine by watering down the leftover 'kaeshi" sweet sauce that I had from serving soba the night before.
Check the color of the eggs after a few hours of marinating. If they appear spotty, roll around the eggs a bit to adjust. For best results, marinate the eggs in a zip bag so that the marinade will coat the eggs evenly.