Rinse the short-grain rice in several changes of cold water until the water runs mostly clear, then drain well. Combine the rice with the water for cooking rice in a medium saucepan, cover, and let soak 20 minutes. Bring to a boil over medium heat, then reduce to low and cook covered until the water is absorbed and the rice is tender, 12–15 minutes. Remove from heat and rest, covered, 10 minutes.
Make the dashi: Combine the kombu and the water for dashi in a saucepan and let sit 10 minutes. Heat over medium until small bubbles appear around the edges (do not boil), 5–7 minutes; remove the kombu. Add the katsuobushi (bonito flakes), simmer 1 minute, turn off the heat, and steep 2 minutes. Strain; you should have about 2 cups dashi.
In a wide skillet or shallow pot, combine the dashi, soy sauce, mirin, sake, and sugar. Add the onion and ginger, bring to a gentle simmer over medium heat, and cook until the onion is tender and translucent, 8–10 minutes, skimming as needed.
Add the beef ribeye, separating the slices into the simmering broth. Cook just until the beef is no longer pink and still tender, 2–3 minutes; skim foam and adjust seasoning to taste.
Fluff the cooked rice and divide into 4 bowls. Spoon the beef, onions, and some broth over each bowl. Top with green onions and beni shoga; add eggs and a pinch of shichimi togarashi if desired. Serve immediately while hot.