In a small bowl, combine dashi, soy sauce, mirin, sake, and sugar.
Pour the sauce into a skillet and add sliced onions. Simmer over medium heat until softened.
Add chicken pieces to the broth and cook for 5–7 minutes, until the meat is cooked through and tender.
Slowly pour the beaten eggs over the chicken and onion mixture. Cover and cook just until the eggs are softly set.
Spoon freshly cooked rice into bowls, then top with the hot chicken-and-egg mixture.
Garnish with chopped green onions and a sprinkle of shichimi togarashi if desired. Serve immediately.