Remove excess skin from the turkey carcass but leave any browned, crispy pieces for additional flavor. To help fit the carcass into a pot, cut it in half, breaking it across the back-bone along the ribs. Place the halves in a large stockpot and add the cold water. Bring to a boil. Boil for 5 minutes, skimming the scum that rises to the top. Reduce heat and simmer for 15 minutes.
Rinse the rice well in several changes of water until water runs clear. Add the rice to the pot. Bring back to a boil, stirring occasionally. Add the ginger. Reduce heat to low, cover, and simmer for about 3 hours, stirring occasionally. (Low heat and stirring are important to avoid scorching as the jook thickens.).
Remove the carcass and skin from the jook. Discard bones and skin. Shred any large pieces of meat or cut into bite size pieces and return them to the soup. Add the salt and simmer for about 30 minutes, until a good consistency is reached. (something like a light- to medium- bodied cream of wheat). Finish with the sesame oil.
Serve with small dishes of garnishes and condiments.