Place the chicken pieces in a large bowl. Add the 1 tablespoon soy sauce, sake, and ginger. Toss well to coat and set aside for 30 minutes or cover and refrigerate for up to 3 hours.
Drain off the excess marinade.
In a medium bowl, whisk together the dashi, soy sauce, mirin, and sugar until the sugar has dissolved.
Place a small 6-8 inch (15-20 centimeter) nonstick skillet over medium heat and add a thin layer of vegetable oil.
Add half of the onion slices and cook, stirring occasionally, until starting to soften.
Add half of the chicken pieces and cook, turning to brown on all sides.
Pour in half of the dashi mixture. Bring the liquid to a simmer and cook until slightly reduced and the chicken has cooked through, 3-5 minutes.
Break two eggs into a bowl and use a fork or chopsticks to very gently mix and break the yolks. There should still be distinct streaks of yolk and egg white.
Reduce heat to medium low and pour the eggs evenly over the chicken.
Shake the pan gently to make an even layer and cook, without stirring, until the eggs are mostly set.
Place a serving of rice in an individual bowl.
Slide the chicken and eggs from the pan over the rice and garnish with the mitsuba or scallions and optionally the Shichimi Togarashi.
Repeat with remaining ingredients to make one more bowl and serve immediately.