Gather the ingredients. Make sure your eggs are at room temperature.
Add enough water to a medium pot to fully submerge the eggs. Add the salt to the water.
Place the pot over high heat and bring to a boil. When the water is at a rapid boil, turn down the heat to low. Use a ladle to place one egg at a time into the pot.
Once all eggs are in the pot, bring the heat back up to high. Set the timer to 6 minutes and 30 seconds. For the first 3 minutes, occasionally gently flip and roll the eggs using a spatula or by turning the handle of the pot left and right - this process helps the yolk to set in the center.
While the eggs are boiling, grab a 32-ounce deli container or quart-sized mason jar. Add soy sauce, water, aged soy sauce, balsamic vinegar, sugar, scallions, chiles, and sesame seeds and garlic if using. Stir vigorously until sugar is fully dissolved.
When the eggs are done cooking, pour off as much hot water as you can, then put the eggs, still in the pot, under cold running tap water to cool them down.
Peel the eggs and add directly to the container with the sauce. The container should be almost full and the eggs should be completely covered by the sauce.
Cover and place the container in the fridge for at least 6 hours to marinate.
Serve one or two eggs, sliced in half, over warm white rice. Drizzle the sauce over the eggs. Store the eggs refrigerated in the sauce and consume within a week.