Break the turkey carcass into pieces and place in a large saucepan with the stuffing, if using, and 1 onion, 1 carrot, 1 celery stick and the seasoning. Add the measured water and bring to the boil. Cover and simmer for 3 hours. Add extra water as necessary.
Remove the carcass and vegetables and discard. Strain the stock and add the turkey meat.
Heat the oil in the rinsed-out pan, then add the potatoes and the remaining onion, carrot and celery. Cook gently, stirring, for 5 minutes.
Pour in the turkey stock and bring to the boil. Simmer for 20 minutes, then add the chestnuts and sherry or port. Reheat and check the seasoning before serving.