Make soup base. In a pot over low heat, saute onions, garlic, ginger, celery, and star anise until soft and translucent, about 5 minutes. Deglaze pan with beef broth. Add soy sauce and mirin. Add the litid, bay leaf, and brown sugar. Bring to a boil and simmer on low heat until the litid softens, about 45 minutes, adding more water if needed.
Add the sotanghon/bihon noodles and simmer until tender.
Arrange the onion leeks, napa cabbage, enoki mushrooms, tofu, and carrots on top and simmer until the vegetables soften for about 10 minutes.
Add the beef sukiyaki strips and boil until the meat is no longer pink. Serve.