In a small bowl, combine the Mizkan bonito soup base (or soy sauce), mirin, and sugar; stir until the sugar dissolves to make the sauce.
Bring the water to a boil in a small saucepan over high heat.
Add the sliced onion, bite-sized chicken pieces, and the prepared sauce to the boiling water; return to a boil, then reduce heat and simmer until the chicken is cooked through, about 2 minutes, skimming any foam.
Pour the lightly beaten eggs over the chicken in a circular motion to cover; reduce heat to low, cover the pan, and cook until the eggs are set but still tender, about 2 minutes.
Stir in the sliced scallion, then divide steamed rice between two bowls and top each with the chicken-and-egg mixture; serve immediately.
