Combine all the listed marinade ingredients in a small airtight container or mason jar until the sugar completely dissolves. Microwave the marinade for 30 seconds if needed to help dissolve the sugar. Set aside.

Fill a small pot with enough water to fully submerge the eggs, then add the salt and vinegar. Bring to a boil over high heat, then reduce to medium-high heat to maintain a steady simmer. Gently lower the room-temperature eggs into the water and immediately set a timer. Boil for 6 minutes for runny yolks, 6 ½ minutes for runny-jammy yolks, 8 minutes for set-jammy yolks, or 10 minutes for fully hard-boiled yolks.

While the eggs boil, prepare an ice water bath in a separate bowl. Immediately transfer the cooked eggs to the ice bath and leave them submerged until completely cold to the touch.

Gently tap the cooled eggs with the back of a spoon to crack the shells. Starting at the wider base where the air pocket sits, slide a spoon under the shell and gently peel it away.

Submerge the peeled eggs in the soy marinade. Place a small piece of paper towel or plastic wrap directly over the eggs to keep the exposed tops in contact with the marinade. Cover and refrigerate for at least 6 hours, preferably 12 to 24 hours for the best flavor.

Remove the eggs from the marinade and cut them in half lengthwise with a sharp knife. Serve cold over hot ramen noodles or rice bowls.