Pour the mirin and sake into a wok or frying pan. Bring to the boil. The initial boiling should remove much of the alcohol taste in the mirin and sake.
Pour in the dashi and soy sauce. Add the sugar. Allow to reach boiling point.
Scatter the sliced onion on the boiling sauce. Spread the sliced chicken over the onions. Bring to the boil. If you see scum rising to the surface, skim it off.
Lower the heat to medium and cook (uncovered to reduce and concentrate the sauce) until the chicken is done. Depending on the size of the pieces and the maturity of the chicken, this will take anywhere from ten to 15 minutes.
Pour the stirred eggs over the chicken. Do this in a circular motion so that the eggs are spread evenly. Sprinkle the scallions over the eggs and chicken. Stir lightly to prevent the eggs from forming large lumps.
When the eggs turn firm along the edges, turn off the heat. Allow the eggs to cook for a minute in the residual heat. This ensures they won’t get overcooked.
Pour the chicken and egg mixture over cooked Japanese rice. Serve the oyakodon immediately.