Bring a saucepan of water to a boil. Once boiling, gently add the eggs using a slotted spoon.
Boil the eggs for 6 minutes for a slightly runny yolk. If you prefer a firmer yolk, boil for an additional minute or two.
While the eggs are cooking, prepare a bowl of ice water. Once the eggs are done, transfer them to the ice water to stop the cooking process. Let them cool for about 5 minutes.
Carefully peel the cooled eggs and set them aside.
In a bowl, whisk together the soy sauce, water, sugar, sesame oil, and rice vinegar until the sugar is dissolved.
Place the peeled eggs in an airtight container and pour the marinade over them, ensuring they are fully submerged.
Add chopped green onions and, if desired, sprinkle sesame seeds over the eggs.
Seal the container and refrigerate for at least 2 hours or overnight for the best flavor.
Serve the eggs as a snack, over rice, or as part of a Korean meal.