Chinese poached chicken breasts with star anise

Chicken second courses

3½ cups canned low-sodium chicken broth or homemade stock 2 carrots, cut diagonally into ½-inch slices 6 scallions including green tops, 5 cut into 4-inch lengths, 1 chopped 6½-inch slices peeled fresh ginger, smashed, plus 2 tablespoons minced fresh ginger 4 cloves garlic, smashed ¼ cup brown sugar, preferably dark ¼ cup soy sauce 5 whole star anise 3 cinnamon sticks 6 black peppercorns ¼ teaspoon salt ¼ cup dry sherry 4 boneless, skinless chicken breasts (about 1⅓ pounds in all)