Cook dumplings in a 6- to 8-quart pot of boiling unsalted water, uncovered, stirring occasionally, until cooked through, 5 to 8 minutes. (Cut into a dumpling to check filling.) Remove pot from heat and keep dumplings warm in hot water. While dumplings cook, bring chicken broth to a boil in a 4- to 6-quart heavy pot. Add cabbage, mushrooms, and carrots and boil, uncovered, stirring occasionally, 3 minutes, then add peas and cook 2 minutes. Stir in scallions, sesame oil, salt, and pepper and boil until all vegetables are tender, about 1 minute. Divide dumplings among 4 soup bowls with a slotted spoon. Ladle soup over dumplings.