Trim off any extra fat on the oxtails. Rinse under running water. Place oxtails in a large cooking pot filled with water, covering them. Soak for 1-2 hours.
Meanwhile, slice daikon radish and cut into bite size pieces. Slice green onions on the diagonal. Set aside soaked oxtails onto a dish, and discard water. Return oxtails to cooking pot, refill pot with 12-15 c. water, broth, or half and half ensuring they are submerged. Bring to this to a low boil. Reduce to simmer.
After 2 hours skim off any foam/fat at the surface of the water. Add sliced daikon radish, salt, pepper, and minced garlic. Simmer 3 hours. Pot can be slightly covered if desired.
5 hours of simmering ensures the oxtails with be very tender. Remove one at a time and place on a cutting board to remove meat and discard bones. Put meat back into pot and stir. Serve soup with cooked white rice, chopped green onion, and kimchi.