One of my favorite things to get at Japanese ramen shops is the ajitsuke tamago, a perfectly soft boiled marinated egg, with the center still a creamy, runny custard. It's all about the timing with these eggs to achieve the right consistency and can take a few tries to get right.
Combine water, sake, soy, mirin, and sugar in a medium bowl and whisk until sugar is dissolved. Set aside
Bring 2 quarts of water and vinegar to a boil in a medium saucepan over high heat. Lower to medium heat once it comes to a boil. Pierce a tiny hole in the bottom of each egg carefully with a thumbtack. This prevents the egg from cracking. Place eggs into boiling water along with egg timer. Cook until egg timer reaches a soft boiled stage.
Remove eggs and run under cold water. Gently place cracks into egg. Remove a little bit of shell from one end. Using small sharp spoon, use to get between egg white and egg shell and remove rest of shell with spoon. You should be able to get most of the shell off in one maneuver.
Put eggs into bowl with marinade. Use spoons or other devices to weight down each egg to keep entire eggs submerged under. Refrigerate and marinate at least four hours and up to 12. Discard marinade after 12 hours. Store eggs in a sealed container in the fridge for up to 3 days. Serve with ramen.
The nutrition information provided are only estimates based on an online nutritional calculator. This is not a comprehensive list of all the nutrients in the recipe (i.e., does not include vitamins, cholesterol, etc). I am not a certified nutritionist. Please consult a nutritionist or doctor for accurate information and any dietary restrictions and concerns you may have.