Arrange the rest of the ingredients on a serving platter and place the platter on the dining table. Put all the sauce ingredients in a saucepan and simmer until the sugar dissolves and it’s hot. Adjust the taste as desired, adding more sugar or mirin for a sweeter taste, or more soy sauce for a saltier taste.
Pour half the sauce into the sukiyaki pan (or cast-iron pan), and then place the pan over a heating source and bring to a boil. Start adding a little of each ingredient to the pot and let cook over high heat until done. Dip each morsel into beaten egg and eat immediately. Continue adding the ingredients and sauce as needed. Add noodles to the pot toward the end of the meal, cooking only to reheat and eat.
If the sauce becomes too thick, add cold water as needed to thin it out.