Cover the turkey carcass in a large stockpot with 12 cups of water. You may need more depending on the size of the carcass. Try to immerse the bird with water, but if your pot isn’t big enough, it’s ok if the back bone sticks out a bit. Add a big pinch of salt to the water.
Bring to a boil and then simmer for 2-3 hours. You may wish to flip the bird once during simmering. The liquid should be reduced by almost half.
Cover the pot (with foil, if the turkey is sticking out) and transfer to the refrigerator overnight.
The next day, remove the carcass from the stock. Pick off any remaining meat and set it aside in a bowl to be added to the soup. Discard the carcass.
If the stock is very gelatinous, place it on the heat over medium-high just until the gelatin melts, and the stock returns to a liquid. Turn off the heat and strain through a fine-mesh sieve.
Give the pot a quick rinse and wipe it out. Return it to the stovetop.