Cover short ribs with cold water and soak, chilled, at least 2 hours. Drain ribs and transfer to an 8-to 10-quart heavy pot with cold water (8 cups). Simmer ribs, partially covered, skimming any foam, 2 hours. Chill ribs in liquid (covered once cool) until fat solidifies, about 4 hours. Meanwhile, soak mushrooms in hot water (4 cups), turning occasionally, until softened, about 1 hour. Squeeze excess liquid from mushrooms and reserve 2 cups soaking liquid; cut off and discard mushroom stems, then halve caps. Discard fat from ribs and return to a simmer. Peel potatoes and cut into 1-inch pieces, then add to ribs with radish, carrots, garlic, dates (if using), soy sauce, fish sauce, molasses, red-pepper paste, mushrooms, reserved mushroom-soaking liquid, and water (if necessary) to barely cover meat and vegetables with liquid. Simmer, partially covered, stirring occasionally, 30 minutes. Stir in onion and scallions and simmer, covered, stirring occasionally, until meat is very tender and vegetables are tender, 15 to 20 minutes. Skim off any fat, then stir in sesame oil. Stir before serving and serve additional red-pepper paste on the side.