procedure

 
Cut beef scraps into 2-inch pieces. Rinse under cold water. Place in a large saucepan along with bones. Add water to cover. Bring to a simmer, skimming off whatever meat scum rises to the surface. When the water is clear, add the sake, the onion, ginger, soy sauce, salt, mirin, and sugar. Simmer until chunks of beef are tender, about 2 hours. Strain through a fine mesh strainer. Pick out beef pieces and set aside. Skim fat off the top of the broth. Alternatively, let soup cool and refrigerate until fat has solidified on top, then scrape off the fat.
When ready to serve, reheat soup in large saucepan in the kitchen, or on a hotplate in the center of the serving table. Add the vegetables and simmer until tender, 10 to 20 minutes depending on the vegetable. Add the tofu during the last five minutes of simmering. Add udon or soba noodles, using cooking times directed on the package. Add beef scraps to reheat.
Meanwhile, beat eggs in individual serving bowls, seasoning to taste with soy sauce.
To serve, either keep broth simmering on a portable stove for the table, or bring the pot to the table. Diners will dip pieces of fatty beef into their individual bowls of egg and soy sauce, along with tofu, vegetables, and noodles.