Crumble the sausage in a 12-inch cast iron skillet, put over medium heat and cook until the fat begins to render out, 2-3 minutes.
Add 1 tablespoon of the butter, the onions, celery, jalapeño, red peppers, a 1/2 teaspoon of the salt, cayenne, and sage. Cook until the vegetables are softened, 3-4 minutes. Fold in the turkey and Sweet Cornbread Pudding or stuffing, Remove to a large bowl.
Return the skillet to the heat and melt 3 tablespoons of the butter. Add the potatoes and the remaining 1/2 teaspoon of salt and cook until tender, 7-8 minutes, then lightly smash with a potato masher or spatula, but leave plenty of chunks.
Spread the turkey mixture on top of the potatoes and press down firmly with a spatula or wooden spoon. Cover and cook for 6-7 minutes, or until the potato layer is browned and crispy.
Remove from the heat and serve topped with fried eggs, if desired.