Drizzle sesame oil in a large stockpot. Add ginger paste, scallion whites, grated carrot, diced mushrooms, minced garlic, chopped quarter of cabbage. Add 4 cups chicken broth, lots of soy sauce, sriracha to taste, black pepper, frozen dumplings. Bring to a boil. Serve with diced scallion greens, extra soy sauce, and sriracha.