Soak the ox bones and beef in cold water for 20 minutes to remove any blood.
Rinse the bones in cold water a couple of times to remove any bone chips.
Drain the water.
Bring 14 cups (3½ qts) of water to a boil in a large pot.
Add the bones and beef and boil for about 10 minutes.
Turn off the heat and remove the bones and beef.
Discard the cooking water.
Rinse and drain the meat and bones in cold water to remove excess fat.
Clean the pot thoroughly before proceeding.
First Broth Pass
Return the bones and beef to the pot.
Add about 12 cups (3 qts) of water, the onion, and the peeled radish.
Bring to a boil over medium heat.
Once boiling (about 20–30 minutes), reduce the heat and simmer for 3 hours.
Remove the beef and radish from the pot, leaving the bones behind.
Place the beef and radish in a bowl and set aside.
Pour the broth into a large collecting bowl and refrigerate while continuing the process.
Second and Third Broth Passes
Refill the pot with about 3 qts of fresh water.
Bring to a boil over medium-high heat, then reduce the heat and simmer for 2½ to 3 hours.
Pour the broth into the collecting bowl.
Refill the pot with water again and repeat: bring to a boil over medium-high heat, then simmer for 2½ to 3 hours.
Pour into the collecting bowl.
Chilling the Broth
Allow the collected broth to cool slightly, then cover with plastic wrap and refrigerate for several hours until the fat solidifies on top.
Serving
Remove the broth from the refrigerator and skim off the solidified fat from the top with a spoon or fine-mesh strainer.
Slice the cooked beef thinly, about ⅛ inch thick.
Cut the radish into ¼-inch-thick slices.
Reheat the broth and ladle it into a serving bowl.
Add a few slices of beef and radish to the soup.
Serve with warm rice and kimchi, along with chopped green onions, minced garlic, kosher salt, and ground black pepper on the side.
Season the soup to taste with salt, chopped green onion, and ground black pepper.
Warm rice can be added directly to the soup if you like — start with 1 tsp of salt and adjust from there.
Spicy Version
Tear about 1 cup of the cooked beef into thin strips and place in a mixing bowl.
Add 2 Tbsp chopped green onion, 2 tsp soy sauce, 2 tsp hot pepper flakes, a pinch of ground black pepper, and 2 tsp toasted sesame oil.
Mix well to combine.
Ladle the hot soup into a serving bowl, add a few slices of radish, and top with the seasoned beef mixture.
Serve with warm rice, kosher salt, and kimchi.