In a wide shallow pan, boil the mirin, sake, soy sauce, sugar, dashi and sliced onion over medium heat. Cook until the onion slices are softened, about three minutes.
Lay the tonkatsu in a single layer in the boiling liquid, making sure that they are at least two inches apart.
Pour the beaten eggs around and between the tonkatsu. Sprinkle in the scallions. Cook just until the eggs are set, about one minute.
Scoop out one piece of pork and the egg around it for each cup of rice. Sprinkle with more scallions.
Serve the katsudon immediately.