Fill a saucepan with enough water to cover the eggs. Place the eggs in the saucepan and bring the water to a boil over medium-high heat. Once boiling, reduce the heat to low and simmer for 5 minutes.
Prepare an ice bath by filling a large bowl with cold water and ice cubes. Once the eggs are cooked, transfer them to the ice bath and let them cool for at least 5 minutes.
Combine the soy sauce, rice vinegar and sugar in a bowl. Stir well until the sugar is dissolved and the ingredients are well mixed.
Peel the eggs and place them in a container or a zip-top bag and pour the soy sauce mixture over them, making sure they are fully submerged. Seal the container or bag and refrigerate for 2 hours to allow the eggs to marinate and absorb the flavors.
When ready to serve, remove the eggs from the marinade and gently pat them dry with a paper towel. Cut the eggs in half lengthwise. Place them on top of the noodles, garnish with sliced green onions, and enjoy!