Step 1

In a small bowl, stir together the soy sauce, sake, sugar, mirin, kombu and 1 cup water. Mix about one-quarter of the sauce into the chicken pieces in a separate bowl and set aside.

Step 2

Heat an 8-inch omelet or donburi pan over medium-high heat. Add 2 tablespoons of the oil to the pan. At the first wisp of white smoke, add half of the onions to the pan and sauté until translucent, about 1 minute. Add half of the chicken and half of the remaining sauce to the pan and stir to combine. Bring to a simmer, then reduce the heat to maintain the simmer. Cook until the chicken is almost cooked through (about 90 percent), about 2 minutes.

Step 3

Crack 2 of the eggs into a small bowl and whisk until combined. Slowly pour in the egg in a steady stream in a circular motion until the chicken and sauce are covered. Reduce the heat to a slow simmer and cover the pan for about 1 minute until the eggs are just set but still very soft.

Step 4

Spoon about 2 cups of the rice into a 9-inch rice bowl and lightly pack it down, leaving about 1 1/2 inches of room at the top. Gently slide the egg mixture onto the rice, making sure not to flip the egg. Garnish with half of the scallions and serve warm. Repeat with the remaining ingredients to make a second bowl.