How to Make It
Melt the butter in a large soup pot. Add the carrots, parsnips, onion, celery root, garlic and a good pinch of salt and cook over moderately high heat for 5 minutes, stirring occasionally. Add the stock and bring to a simmer. Add the turkey carcass and bones and the bay leaves and bring to a simmer, skimming as necessary. Reduce the heat to low, cover partially and simmer for 1 hour.
Remove the turkey bones and carcass from the soup and let cool slightly; discard the bay leaves. Refrigerate the turkey and the soup separately overnight. Skim the fat off the surface of the soup and reserve for making the dumplings.
Measure the reserved turkey fat and add enough butter to make 1/2 cup, then transfer to a medium saucepan. Add the milk and bring to a simmer over moderately high heat. Season with the salt, pepper and nutmeg. Remove from the heat and, using a sturdy wooden spoon, stir in the flour until the dough is smooth and pulls away from the side of the pan. Add the tarragon, then beat in the eggs 1 at a time and stirring until fully incorporated between additions.
Bring the soup to a simmer. Drop tablespoons of the dumpling dough into the soup and simmer for 10 minutes, until firm. Add the diced turkey to the soup and cook for 1 minute. Ladle into shallow bowls and serve.