Place short ribs in a large bowl and fill with water. Allow short ribs to sit for 30 minutes. Drain.
Place short ribs in a large pot and fill with water until ribs are just covered.
Place pot over stove and bring to a boil over medium-high heat. Boil ribs for 20 minutes.
Transfer short ribs to a plate, drain water and clean pot.
Whisk together soy sauce, sugar, grayed pear, garlic, mirin, sesame oil, and black pepper.
Place ribs back into the pot along with braising liquid and toss together.
Add water, cover pot and bring to a boil over medium-high heat. Boil for about 30 minutes.
Add potatoes, carrots and radish to the pot, cover again and simmer for about 25 minutes.
Add mushrooms and simmer, uncovered, for about 10 minutes.
Sprinkle short ribs with green onions and serve with steamed rice.