Combine 2 cups water, the broth, ham, sherry, sugar, ginger, orange zest, 1/2 teaspoon salt, and pepper to taste in a large pot. Cover and bring to a boil over high heat.
Add the scallion whites, mushrooms and carrots. Reduce the heat and simmer, uncovered, until the carrots are crisp-tender, about 4 minutes.
Add the cabbage, dumplings and scallion greens. Cover and cook until the dumplings are soft and heated through, 4 to 5 minutes. Divide the dumplings and soup among bowls.