Open abura-age and place in a colander. Pour boiling water over deep-fried tofu to remove any excess oil. Allow to drain.
At the table, set cooking pot on a portable stove in center of table. Fill with chicken stock, add soy sauce and mirin, season to taste with salt, and bring to a simmer over medium heat.
Divide remaining cooking ingredients, except noodles, into thirds. Keep chilled until ready to cook.
Add about one-third of the potatoes, daikon, carrots, leeks, cabbage, mushrooms, burdock, grilled tofu. chicken, fried tofu, and bok choy to simmering broth.
Cook until vegetables begin to soften and chicken is just cooked through, about 5 minutes. Add about one-third of the beef.
Simmer until just cooked through, about 1 minute. Serve cooked items to guests.
Repeat with second 1/3 of the cooking ingredients.
Repeat with remaining third of the cooking ingredients.
Once all the vegetables, tofu, chicken, greens, and beef have been eaten, use a small sieve to pick out scraps. Bring remaining broth in pot back to a simmer, add noodles, and simmer until cooked through, 6-8 minutes. Serve in individual bowls.