In a large saucepan, combine the broth, carrots, the 5 scallions, the smashed ginger, the garlic, brown sugar, soy sauce, star anise, cinnamon sticks, peppercorns, and salt. Bring to a boil, reduce the heat, and simmer, covered, for 20 minutes.
Add the sherry and chicken and bring back to a simmer over moderately low heat, covered. Turn the chicken and simmer, covered, until the chicken is just done, about 5 minutes.
With a slotted spoon, transfer the chicken, carrots, and star anise to large shallow bowls. Strain the broth and add the minced ginger and 2 tablespoons of the chopped scallion. Ladle the broth over the chicken and top with the remaining chopped scallion.
Wine Recommendation: The exotic yet delicate broth requires a flavorful but light white wine. A German riesling would be ideal; if the riesling you choose has some slight sweetness, all the better.