Whisk together soy sauce, sake, coconut sugar, rice vinegar, and water.
Add all the liquid to a small sauce pan and heat the liquid until it starts to simmer (~1 minute). Take it off the stove and let it cool for 20 minutes. Cooling the liquid will prevent the heat from cooking the eggs.
Put the soy sauce mixture into a bowl or ziplock bag. Set aside.
Soft boiling the eggs: Bring a pot of water to a boil. Once at a rolling boil, cook eggs for 6 minutes 10 seconds. After this time, immediately put the eggs in ice water. Let them sit for 5 minutes in the ice water.
De-shell the eggs and add it to the soy sauce mixture. Marinate for 1 hour or more. If the egg is not fully submerged in the sauce, marinate for 30 minutes on one side and then flip it over and marinate for another 30 minutes on the other side.