In a medium bowl, whisk together the water and sugar until the sugar dissolves, then stir in the sherry vinegar and soy sauce.
Bring a large pot of water to a boil. Carefully put the eggs into the boiling water and cook for exactly 6 minutes and 50 seconds, stirring slowly for the first 1.5 minutes so the heat distributes evenly. Meanwhile, fill a large bowl with cold water and ice.
When the eggs are done, transfer them to the ice bath.
Once the eggs are cool, peel them in the water so the exteriors stay smooth. Transfer them to the soy sauce mixture and marinate in the fridge for at least 2 hours and up to 6 hours, completely submerged. If necessary, top the eggs with a small plate to keep them under the liquid.
Remove the eggs from the marinade. Refrigerated in a tightly sealed container, they keep for up to a month.
To serve, cut the eggs in half lengthwise and season with salt and pepper.
Notes
Adapted slightly from Milk Bar Life by Christina Tosi.
The soy sauce in the original is low-sodium. With regular-strength soy sauce, marinate for less time.
The soy sauce mixture can be saved for another batch of eggs.