1. Add the eggs to a pot filled with water. Fill a small pot with room temperature water and place it on a burner. Gently lower the eggs (to prevent them from cracking) and turn the heat on.
2. Boil the eggs. Bring the water to a boil, lower the heat to a bubbling simmer and cook for 6 minutes for a runny center, or 7 minutes for a firmer, jam-like center. 
3. Make the marinade. While the eggs are boiling, whisk the ingredients for the marinade in a bowl and set aside.
4. Cool the eggs in an ice bath. Once the eggs are cooked, submerge them in a bowl filled with ice and cold water. Let them cool for about 5 minutes. Keep the water for peeling the eggs!
5. Peel the eggs. Crack the shells by gently tapping them on the counter and return the eggs to the ice bath. Peel them submerged in water. I find this method to be the easiest and most successful. 
6. Marinate. Place the eggs in a storage bag and add the marinade. Close the bag and put the bag on a plate or in a bowl, in case it leaks. Refrigerate and let the eggs marinate for 2-4 hours. Rotate the eggs every 30 minutes so they are evenly flavored. You can let them marinate for up to 24 hours for a stronger taste.
7. Serve. Slice in half and serve with ramen or rice.

Using an Egg Cooker. If you are using an egg cooker, use the designated cup and add water to the medium marker, or just under it for a softer consistency. Put the lid on and start steaming.