Heat a heavy thick-bottomed pot on the stove.
With the heat on medium, spread the fatty beef on the pan.
Cook for a minute or so without disturbing then stir and continue cooking just until no longer pink.
Push the beef to one side of the pot and arrange the mushrooms, bok choy, carrot and narutomaki on the empty space.
Turn up the to high, stir together all the ingredients for the sukiyaki sauce, pour into the pot and allow to boil. Cook everything for two to three minutes, pushing down the solid ingredients into the sauce.
Using kitchen tongs or a pair of chopsticks, lift out the beef, mushrooms, bok choy, carrot and narutomaki, divide and arrange in four bowls.
With the heat still on, drop in the drained noodles into the sauce and cook for two to three minutes.
Scoop out the noodles and divide among the four bowls.
If adding mung bean sprouts, add them now.
Taste the sauce. If it's too strong, add a little water and allow to boil.
Carefully ladle the hot sauce into the bowls.
Sprinkle in scallions.
Serve your sukiyaki immediately.