Discard the turkey skin. Scrape the herbs and all the stuffing from the turkey carcass carefully, especially if sage was used. Break up the carcass. Put it in a tall straight-sided 4-quart soup pot and add the water to cover. If that amount doesn’t cover, the pot is too wide. Bring to the boil and skim off the foam. When the broth is clear, add the carrot, whole onion, and celery. Cover and simmer for 1 hour.
Remove the carcass. Pick off meat and dice it. Discard the vegetables. Strain and skim stock and return the turkey meat to it.
Heat 2tablespoons butter with the bacon or ham. In the combined fat slowly sauté the garlic, chopped onion, green pepper, and okra until golden brown and okra is no longer stringy, about 25 minutes. Add to the soup along with tomatoes, thyme, bay leaf, and cayenne.
Simmer the soup gently for 30 minutes, adjusting seasoning as you do so.
Heat the remaining 4tablespoons butter in a small heavy-bottomed saucepan. When bubbling, add the flour and stir until smooth. Cook very, very slowly, stirring almost constantly, for about 10 minutes, or until the roux is a dark coffee color. The flour will seem to take a long time before it begins to color, but once it does it burns quickly, so give it your undivided attention. When the roux is a good dark espresso color (but not burned), cool slightly, then stir it into the simmering soup. Cook 30 minutes more.
Adjust the seasoning and serve in a bowl with a mound of white rice heaped in the center of each serving.