In a Dutch oven combine broth, ginger, and soy sauce. Bring to boiling; reduce heat. Simmer, covered, for 5 minutes.
Add carrots; simmer for 3 minutes. Stir in noodles. Bring to boiling; reduce heat. Simmer, uncovered, about 4 minutes or until noodles and carrots are tender.
Stir in chicken, bok choy, peapods, radishes, and sesame oil; heat through.