The turkey, roast and ham should be cubed from the leftovers remaining from the Christmas Day lunch. In a heavy bottom black iron pot, heat oil over medium-high heat. Add flour and using a wire whisk, stir until golden brown roux is achieved.
Add onions, celery, bell pepper and garlic. Sauté 3 to 5 minutes or until vegetables are wilted. Add meats and blend into the roux mixture. Add hot stock, one ladle at a time until stew-like consistency is achieved. Add basil and thyme.
Bring to a rolling boil. Reduce to simmer and cook until meat is falling apart, approximately 30 minutes. Add potatoes, carrots, green onions and parsley. Return to a simmer and season to taste using salt and pepper. Cook until potatoes are tender, adding additional stock if necessary to retain consistency. Serve over steamed grits.