Soak the beef bones. Add the beef bones to a stockpot. Add enough cold water to cover. Place a lid on top and set aside in a cool place (fridge or cold kitchen counter) to soak for 30 minutes. During this process, the blood will seep out of the meat and bones. Drain and add the beef bones back to the pot.
Prep the vegetables. Peel the onion and trim the ends, making sure to keep it whole (for easier removal). Peel the radish and cut into two large chunks. Finely mince the green onion and set aside.
Parboil the beef bones. Add enough cold water to cover the bones. Bring to a boil over high heat until the fat and scum rises to the surface, about 5 minutes.
Drain and rinse. Using a colander, drain the bones. Rinse under cold water, using your hands to wipe away any residual fatty bits or scum clinging to the meat and bones. Also, make sure to wash the pot thoroughly.
Cook. Add the clean beef bones back to the clean pot. Add 13 cups of cold water, onion, radish (mu), dried kelp (dasima), soy sauce, and beef bouillon powder (dashida). Bring to a boil over high heat, then lower heat to medium. Remove any residual fat or scum that floats to the surface. Cook, uncovered, until the beef is tender but not yet falling off the bone, about 60 minutes. Cover and cook until the meat is falling off the bones, another 15-30 minutes depending on the thickness of the meat.
Remove aromatics. When the meat is tender and falling off the bone, remove the onion, radish and dashima. Discard the onion and dashima. Reserve the radish and set aside.
Optional: Refrigerate Overnight. For a less oily broth, refrigerate the soup overnight. The fat will harden and be easier to remove.
Add Dangmyeon + Garlic. Add the sweet potato noodles directly into the soup. Add the minced garlic. Cook until the noodles tender yet slightly chewy, about 5-7 minutes.
Add cooked radish. While the Dangmyeon cooks, slice the cooked radish into thin 1/2-inch half moons. Add the radish pieces back to the soup pot.
Taste and adjust seasoning. Taste the soup and adjust seasoning. Add more salt or a pinch or two of beef bouillon powder if needed.
Serve. Transfer the soup to individual soup bowls. For each portion, add 1-2 beef ribs, noodles, radish, and soup. Garnish with black pepper and green onion. Serve immediately with rice and kimchi. Enjoy!