Bring chicken broth to a low boil in a large pot. Add ginger and garlic, cover, and cook for 5 minutes. Add the bok choy and partially cook 5 minutes, then add the frozen wontons and mushroom, simmer for another 3-4 minutes, or until the wontons are heated through and bok choy is tender and wilted. Stir in soy sauce, sesame oil, and honey ginger balsamic. Serve immediately.