Thinly slice the onions and green onions, separating the whites and greens. Cut the beef into bite-sized pieces.
Make the sauce: In a small container, mix all the sauce ingredients until combined. (For an alcohol-free version, mix 1 ¾ cups of water, 6 tablespoons of soy sauce, 1.5 tablespoons of sugar, and 1.5 teaspoons of Hondashi.)
Pour the sauce into a large pot. Add the sliced onions and white parts of the green onions. Bring it to a boil. Once it starts boiling, reduce the heat to medium and simmer for 2 minutes or until the onions turn translucent.
Add the beef to the pot, gently separating any pieces that are sticking together. Cover with a lid and simmer for 5 minutes or until the beef is tender. (If the beef isn't tender enough, add a splash of water and simmer a little longer.)
Optionally, for a cleaner broth, skim off the foam or any impurities as it simmers.
To serve, divide the rice into serving bowls. Using chopsticks or tongs, place the beef and onions on top of the rice. Drizzle with 1 or 2 tablespoons of the broth. (Don't discard any leftover broth. You can add some mushrooms or tofu, simmer, and enjoy as a second rice bowl.)
Add some pickled ginger (if using), green onions, and soft-boiled eggs (if using) on top. Enjoy!
