Pour the chicken broth and ginger into a large stockpot and bring to a simmer over high heat. Add the chicken breasts, allow the broth to return to a simmer, about 4 minutes, then lower the heat to medium-low and simmer gently, partially covered for 5 minutes until the chicken is just cooked through. Turn off the heat, remove the chicken with a slotted spoon and let it cool for about 5 minutes on a plate.
Meanwhile, return the broth to a simmer over medium-high heat, add the edamame and allow the soup to come back to a simmer again, about 3 minutes. Add the udon noodles and 1/2 teaspoon of hot sauce. Cook according to the noodle package directions (usually 6 to 7 minutes), stirring frequently until the noodles are just soft but not mushy, and the edamame is tender.
While the noodles are cooking, shred the chicken using your fingers or two forks if you prefer, adding it to the soup as you shred it. As soon as the noodles are tender, stir in the scallions and turn off the heat.
Serve hot, with additional hot sauce if desired.
Note: Dried udon noodles are available in many supermarkets now, as well as online and in Asian specialty food stores. They are made from wheat flour, and when cooked up they are thick, chewy and soft. They are often featured in Japanese dishes, and usually come in 10 ounce packages (use 2 of the 3 noodles bundles) or 12.8 ounce packages (use 2 of the 4 noodle bundles). You could substitute spaghetti or linguine instead, though the cooking time will be longer.