Add the gosari and water to a small pot. Boil. Turn the heat off and let it cool in the cooking water. When ready to use, rinse in cold water and drain. Cut into 4-inch lengths.
In a large pot, bring the meat, onion, and optional radish, to a boil in water. Reduce the heat to medium, and skim off the scum. Boil, covered, until the meat is tender.
Throw in the bean sprouts and scallions, and boil over medium heat. Add salt and pepper to taste. Slowly drizzle the optional eggs over the boiling soup. Serve.