Add the gosari and 4 cups of water to a small pot. Boil over medium heat, covered, until tender. Mine only took about 30 minutes, but the time can vary significantly depending on gosari. 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, removing tough ends of the stems, if any.
In a large pot, bring the meat, onion, optional radish, and garlic to a boil in 14 cups of water. Reduce the heat to medium, and skim off the scum. Boil, covered, until the meat is tender enough for shredding, 1 to 1-1/2 hours. Pull a string of meat off and check the tenderness. Remove the meat and cool. Discard the vegetables, reserving the stock in the pot. Spoon off any visible fat.
When the meat is cool enough to handle, shred into about 3 to 4-inch strips.
Blanch the bean sprouts in boiling water for a minute. Wash with cold water and drain. Cut the scallions into 4-inch lengths. Thinly slice the soaked mushrooms.
In a pan, heat the sesame oil until hot over low heat and stir in the chili pepper flakes. Turn the heat off as soon as the oil starts to turn red and the chili pepper flakes become a bit pasty. This only takes a few seconds. Do not burn the flakes.
Add the meat, fernbrakes, mushrooms, 1 tablespoon soup soy sauce, and garlic. Combine well.
Add the meat and gosari mixture along with 1 tablespoon of soup soy sauce into the broth. Stir in the gochujang and doenjang and boil over medium heat, covered, for 20 minutes.
Throw in the bean sprouts and scallions, and boil for another 10 minutes. Add salt (1 teaspoon or more) and pepper to taste. Slowly drizzle the eggs over the boiling soup and turn the heat off. Serve with rice.
You can also soak the gosari for several hours to soften and then boil over medium heat until tender.