Shoyu Tamago

In a saucepan, mix the water, soy sauce, mirin, rice vinegar, and jalapeño and bring to a simmer. Simmer for 3 minutes, the remove from the heat. Set aside to cool.

Boil the eggs: Bring a pot of water to a boil over medium-high heat. Reduce the heat to medium and carefully lower the eggs into the water. Gently stir, regularly, during the first few minutes of cooking so that when you cut the eggs in half, the yolks are centered. (Alternatively, lay the eggs sideways overnight.) Boil the eggs to your liking: 6 minutes total for soft-boiled to 9 minutes for medium-boiled (or up to 11 minutes for hard-boiled).

Drain and rinse the eggs under cold running water to stop the cooking process. Crack the shells, carefully peel the eggs, and rinse. Set aside.

Pour the marinade into a container large enough to hold all of the liquid plus the eggs (about 1 qt / 1 L). Transfer the eggs to the marinade and let sit in the refrigerator for at least 3 hours and up to overnight. Remove the eggs from the marinade, cut in half lengthwise, and serve. The eggs, removed from the marinade, can be kept in a covered container in the refrigerator for up to 3 days. The marinade can be kept (and reused) for up to a week.