Soak the short ribs in cold water for about 1 hour to draw out excess blood, changing the water 2–3 times. Drain well.
Add ribs to a large pot and cover with fresh water. Bring to a boil and cook for 5 minutes. Drain and rinse the ribs thoroughly.
In a blender, combine the Asian pear, onion, garlic, soy sauce, honey, mirin, beef broth, sesame oil, and black pepper. Blend until smooth.
Place the ribs in a heavy pot or Dutch oven and pour the blended sauce over them. Add enough water for the ribs to be 80% covered. Bring to a boil, then reduce to a gentle simmer.
Cover and cook for about 1 hour, skimming off excess fat occasionally.
Uncover the pot and add the radish, potatoes, and shiitake mushrooms. Cover again and simmer for another 35–40 minutes, or until the ribs are tender and the vegetables are soft.
Garnish with sliced scallions and serve hot with rice.