Place the beef shank, tendon, ginger, scallion, salt, Shaoxing wine, and water into a pot and bring to an active simmer.
Once the water starts to simmer a bit of scum may form on top, skim it off with a spoon or ladle. Cover the pot and maintain at an active simmer
After approximately 1 hour, the shank will be finished cooking. The shank should still be quite firm and just starting to soften slightly. Do not allow the shank to cook until fully soft and tender. Remove the shank from the pot and place it in a bowl of cool water. Allow the tendon to keep cooking at an active simmer for 2-3 more hours, covered.
After the beef shank has been in the bowl of cool water for 10 minutes, add plenty of ice to the bowl and allow the shank to cool in the ice water for 20 minutes. Remove the shank from the ice water and place it in the refrigerator until ready to use.
The beef tendon should be done after about 2-3 hours of additional cooking time (3 to 4 hours of total cooking time). Unlike the beef shank, the tendon should be very soft and gelatinous when it is done. It will firm up considerably when cooled.
Cool the beef tendon by submerging it directly into a bowl of ice water until totally firm, about 30-40 minutes. Both the shank and tendon can be cooked ahead of time and stored in the refrigerator, covered, for up to 3 days.