Place the turkey carcass, neck (if you haven't cooked it with the turkey), leftover skin and bones into a large stock pot (at least 8 to 12 quarts depending on the size of the turkey), and cover with cold water by an inch. Add any drippings that weren't used to make gravy and any giblets (not the liver) that haven't been used already. Add thickly sliced onion, chopped carrots, celery, celery tops, parsley, thyme, a bay leaf, and some peppercorns to the pot.

Bring to a boil on high heat, and then lower the heat to keep the stock to a bare simmer. As it simmers, skim off any foamy crud that may float to the surface of the stock from time to time.

Add about 1 teaspoon of salt and ½ teaspoon of ground black pepper depending on how big your turkey is.

Simmer the pot partially uncovered, continuing to skim off any foam that comes to the surface.

After 4 hours of a low simmer, remove the bones and vegetables from the pot. Then strain the stock through a fine mesh sieve or strainer.

Heat butter or olive oil (or turkey fat rendered from the stock) in a large pot on medium-high heat. Add the carrots, onions, and celery. Cook until the onions are softened, about 10 minutes.

Add garlic and cook for a minute more, until fragrant. Add the stock to the pot. Add the parsley, poultry seasoning, and salt and pepper to taste. Cook until the vegetables are cooked through.

Add the noodles or rice If adding noodles and cook until al dente, about 4 minutes. If adding rice, cook for 15 minutes.

Take some of the remaining turkey meat you reserved earlier, shred it into bite-sized pieces, and add it to the soup. Cook for 1 more minute to warm the turkey meat. Add salt and pepper to taste.