How to Make It
In a large pot of boiling, salted water, cook the pasta until just done, about 3 minutes. Drain. Rinse with cold water and drain thoroughly.
Heat a large nonstick frying pan over moderately high heat. Add the oil and sprinkle the sugar into the pan. Let sit until the sugar begins to turn golden brown, about 1 minute. Stir until the sugar turns a medium brown. Add the steak, in about five batches, turning quickly with tongs, until browned and just done, 1 or 2 minutes in all. Remove. The sugar should glaze the beef with brown caramel. If the pan gets too hot, reduce the heat to moderate so the sugar won't burn. Add the scallions; cook, stirring, until browned, about 2 minutes.
In the pasta-cooking pot, combine the pasta, the beef and any accumulated juices, the scallions, broth, soy sauce, sake, tofu, cabbage, and mushrooms and bring to a simmer. Simmer, stirring, until the vegetables are almost tender, about 2 minutes. Add the spinach and continue cooking until wilted, about 30 seconds longer.