In a large saucepan bring 6 cups water to boiling. With a spoon place frozen wontons, one at a time, in the boiling water. Return to boiling; reduce heat. Simmer, uncovered, 5 minutes. Drain; rinse with cool water.
Meanwhile, in a medium saucepan combine chicken broth, carrot, green onions, and ginger. Bring to boiling; reduce heat. Simmer, covered, 2 to 4 minutes or until vegetables are crisp-tender. Remove ginger and discard. Stir in sesame oil. Divide wontons among bowls; ladle broth mixture over wontons. If desired, sprinkle with cilantro.