Pick as much meat off the turkey carcass as possible, and reserve it for soup or turkey salad.
Place the whole turkey carcass in a large stockpot. Add large chunks of vegetables, a few whole spices, and herbs.
Fill the stock pot with cold water to cover the ingredients by about an inch.
Place the pot on the stove over medium heat. Once the water reaches a fairly active simmer, adjust the heat so the liquid bubbles gently. You do not want the stock to boil, which will lead to too much evaporation.
Also, the proteins and fats being released from the bones can emulsify and make the stock cloudy. This will not affect the final flavor of the dish, but if you want a pretty and clear stock, make sure the stock does not boil.
As the stock simmers, a layer of grayish protein foam will rise to the surface. Carefully skim this off with a large spoon or a ladle.
Let the stock simmer for several hours, adding as much water as necessary to maintain the volume. However, you should not have too much evaporation if you have maintained a slow simmer.You will know when the vegetables and bones have given up all of their flavors when you can snap a small turkey bone in half with minimal effort. Strain the stock through a fine strainer, pressing down on the solids. Discard the solids, and strain the stock again. If you use the stock immediately, carefully skim off the fat that rises to the top. If not, leave the fat on, as it can be more easily removed when solidified.
You will want to chill the stock very quickly. You can carefully pour the stock into a metal bowl inside a larger metal bowl that has ice in it (an ice bath) and stir until the stock has cooled.