Heat a large cast iron pot (such as Le Creuset) on medium heat. When the pot is hot, add the cooking oil.
Add the sliced beef and sprinkle the brown sugar. Stir and sear the meat. When the beef fat starts to render, add the onion slices.
Once the meat begins to brown, add the mushrooms. Add equal parts of sukiyaki sauce and dashi to cover the ingredients.
Add the hakusai. Add equal parts of sukiyaki sauce and dashi to cover the ingredients.
Add the tofu. Add equal parts of sukiyaki sauce and dashi to cover the ingredients.
Add the shirataki noodles. Add equal parts of sukiyaki sauce and dashi to cover the ingredients.
Add the shungiku and pour the rest of the sukiyaki sauce and dashi. Put the lid on the pot and bring to a boil on medium heat, about 15 minutes.
Once boiling, turn the heat down to low, add salt to taste (or add dashi if the sauce is too salty). You can add the udon now, or after everyone has taken their first serving. Cook until the udon is heated through, and serve.