1 (15- to 16-oz) package frozen Asian dumplings (also called pot stickers; about 20 to 24)
5 cups reduced-sodium chicken broth (40 fl oz)
3 cups thinly sliced Napa cabbage (from 1 head)
2 cups sliced shiitake mushroom caps
1 cup shredded or matchstick (1/8-inch-thick) carrots (from a 10-oz bag)
1/2 cup frozen peas
1/2 cup chopped scallions
1 teaspoon Asian sesame oil
1/2 teaspoon salt
1/8 teaspoon black pepper
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.
Makes 4 main-course servings.