Add the sausage to a heavy skillet over medium-high heat and cook until the sausage begins to render some of its fat, about 2 to 3 minutes.
Add the onions, jalapeno, and peppers to the sausage, and cook until soft and translucent, 3 to 4 minutes. Add the potatoes to the skillet and increase the heat to high. Cook until the potatoes have browned lightly, another 3 to 4 minutes.
Add the black beans, leftover pudding or stuffing, and turkey, and stir occasionally. Cook until the hash is thoroughly heated, 3 to 4 minutes. Season with cayenne, salt, and pepper, to taste.