Crack the eggs and separate the yolks from the whites.
Carefully place the separated yolks onto a plate.
Mix soy sauce, water, mirin, and sugar to make the marinade.
Bring the marinade to a boil and let it cool.
Pour the cooled marinade over the yolks to fully submerge them.
Cover with plastic wrap and let them marinate in the refrigerator for at least 6 hours.
Serve the marinated yolks over rice.