Soak the oxtail: Place the oxtail in a large bowl of cold water and soak for 1 hour. This draws out blood and impurities, and the water should turn pink.

Blanch the oxtail: Bring a large pot of water to a boil and add the oxtail. Boil for 5 minutes, skimming off the gray foam that rises to the surface.

Rinse thoroughly: Drain the oxtail and rinse each piece under cold running water. Scrub off any remaining scum until the water runs clear.

Start the broth: Add the rinsed oxtail to a clean large pot with 5 quarts of fresh cold water. Add the onion, garlic and ginger.

Bring to a boil: Bring the pot to a boil over high heat, then immediately lower to a gentle simmer. A hard boil will make the broth greasy instead of smooth.

Simmer low and slow: Simmer uncovered for 3 to 4 hours, skimming fat from the surface every 30 minutes or so. The broth should gradually turn from clear to a soft milky white.

Add the radish: If using daikon, add it to the pot during the last 45 minutes of simmering. It should soften but still hold its shape.

Check the color: The broth is ready when it looks opaque and milky white, not thin or clear. If it's still thin, continue simmering another 30 to 45 minutes.

Remove the oxtail: Lift the oxtail pieces out of the pot and let them cool slightly on a plate. Strain the broth through a fine mesh strainer if you want a cleaner finish.

Shred the meat: Pull the meat off the bones with a fork, discarding bones and excess fat. Return the shredded meat to the strained broth.

Assemble the bowls: Place a scoop of cooked rice in each bowl and ladle the hot broth and meat over the top. Garnish with sliced green onions.

Season at the table: Serve with salt and black pepper on the side so each person can season their own bowl to taste.