Cover bones in cold water, just enough to cover, and let sit for 1 hour. Blood and fat particles will leach out. Drain the bloody water and rinse the bones under cold running water.
Now it's time to parboil the bones. Cover with cold water (again), just enough to cover. Bring to a boil and vigorously boil for 5 minutes. Scum and other impurities will rise to the surface.
Drain the pot. Wash the pot thoroughly with soap and water. Then wash the bones with cold water, one by one, until the bones look clean. Place clean bones into the clean soup pot.
Add 20 cups of cold water, and 2 large, peeled onions to the clean soup pot and clean, parboiled beef bones. Cover and bring to a boil, then lower heat to a vigorous simmer. This is not a roiling boil with big bubbles breaking at the surface; this is a vigorous simmer with lots of small bubbles popping up all over.
After 3 hours of vigorous simmering (covered), add beef tendon and simmer until soft, about 1 more hour (covered). Depending on the thickness of the tendon, this can take longer so poke with a chopstick to check for tenderness. The tendon should be soft enough so that there's some resistance, but not too much.
After a total of 4 hours cooking time (3 hrs for the bones, 1 more hour with added tendon), the soup should look milky. Discard onion and beef bones. Remove beef tendon and slice into bite-sized pieces when cool enough to handle. Add tendon back into the soup pot.
If possible, refrigerate overnight. This will allow the fat to harden. The next day, remove the hardened fat and discard. (This is an optional step but will result in a less fatty soup.)
Season soup with salt. Then serve with a generous amount of chopped green onion, freshly cracked black pepper, and additional salt for people to add at the table. Rice and kimchi make perfect accompaniments.