In a pot, combine soy sauce, mirin, water, dried kelp, and sugar.
Bring to a boil then reduce to a simmer for 2 minutes. Remove from heat and set aside to cool completely.
While the soy sauce brine is cooling, prepare the eggs. Separate the egg yolks from the egg whites. Place the egg yolks in a container, preferably glass. one. Do not overcrowd the container - the egg yolks should be in a single layer with room to move around.
Once the soy sauce brine has cooled, strain the kelp. Carefully pour the brine into the container with the egg yolks. Be careful not to pour the brine directly onto the egg yolks. Instead, pour it in at the corner or side to prevent the egg yolks from popping.
Cover the container and place it in the fridge for at least 12 hours or up to 48 hours. To ensure both sides of the egg yolks are evenly cured, flip the egg yolks every 12 hours. Alternatively, you can lay a sheet of paper towel on top of the eggs and gently press down until it is soaked in the brine. This will ensure that the top of the egg yolks is fully submerged for an even cure. If you use the latter method, you won't need to flip the eggs every 12 hours!
*Note: The egg yolks will form a gel-like consistency the longer they sit and cure in the soy sauce brine. If you prefer a runnier egg yolk, the eggs should be ready to eat within 12 to 24 hours.
Serve with a fresh bowl of rice and your favorite toppings, like scallions and nori.