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1
For Kanto style, combine soy sauce, mirin, sake, dashi, and sugar in a small saucepan. Warm over medium heat, stirring until the sugar dissolves completely. Taste: the warishita should be decidedly sweet and savory in balance, neither sour with raw sake nor sharp with undissolved sugar. Set aside. For Kansai style, no warishita is prepared; seasoning proceeds directly in the pan at the moment of cooking.
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2
Set the sukiyaki-nabe (cast iron skillet) over the table burner at high heat. The pan must be very hot before any ingredient is added; a drop of water should evaporate on contact immediately. For Kansai style, rub the hot pan thoroughly with the piece of beef suet until a thin film of rendered fat coats the surface. For Kanto style, add a small amount of the warishita to the empty pan and allow it to heat through before the first additions.
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3
This is where the dish lives or dies. For Kansai style: lay 2–3 slices of wagyu in a single layer in the fat-coated pan. The beef should sear audibly on contact. Sprinkle sugar directly over the beef, then add sake and soy sauce to the pan in stages, not all at once — the seasoning is adjusted throughout the meal, not fixed in advance. For Kanto style: add a ladleful of warishita to the hot pan and arrange a first batch of beef slices in the broth. In both styles the beef is cooked in small quantities; crowding the pan drops the temperature and prevents proper flavor development. The beef is done when it has just lost its raw color — it should not be cooked beyond this point.
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4
Add the prepared vegetables and yaki-dōfu to the pan in separate areas, keeping the shirataki physically apart from the beef to prevent the calcium compounds in the konnyaku from toughening the meat. Naganegi, enoki, mitsuba, and yaki-dōfu may share space with the beef; shirataki is placed to one side. For Kanto style, add further warishita as needed to maintain a shallow, gently simmering broth. The naganegi is ready when translucent and slightly softened at the edges; the yaki-dōfu when warmed through and lightly colored by the broth.
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5
Monitor the broth throughout. As it reduces, it concentrates and becomes progressively sweeter. Add small amounts of dashi or hot water to the pan whenever the broth thickens noticeably or the sweetness becomes excessive. The correct broth consistency is that of a light, glistening sweet soy — not a thick glaze, not a dilute soup.
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6
Add the shungiku only in the final moments of each cooking round. Lay the greens over the surface of the broth and cover briefly; they are done the instant they wilt and turn a deeper, vivid green. Prolonged cooking destroys their bitter-herbal freshness, which is their sole purpose in the dish.
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7
Each diner beats a whole egg in an individual bowl and holds it at table. Every piece of cooked beef, tofu, or vegetable is lifted from the pan and passed through the beaten egg before eating. The egg should be at room temperature; a cold egg cools the sukiyaki piece too rapidly and does not coat it smoothly. The egg is ready to receive when it is fully beaten and uniform — no streaks of white remaining.