In a large Dutch oven, combine broth, garlic and ginger. Season chicken with salt and pepper, and add to pot. Bring to a boil over high, skimming the foam and fat that rises to the top and discarding it. Reduce heat to medium-low and cook, occasionally stirring and skimming, until foam no longer appears in the broth, about 5 minutes.
Step 2
Add mushrooms, cabbage, daikon, scallions and carrot to the pot, arranging them in sections, and season with salt. Cover and simmer over medium to medium-low heat (maintain a good simmer, but do not boil) until chicken is cooked through and vegetables are tender, about 10 minutes. Discard ginger. Season to taste with salt and pepper.
Step 3
Meanwhile, in a small bowl, combine ponzu, sesame oil and yuzu kosho (if using), and mix well.
Step 4
Divide donabe among four bowls. Drizzle with some of the ponzu sauce and serve warm.