Preheat the Oven to 400 degrees F. In a medium pot, cook the apples, onion, oil, and 1 tablespoon of the butter over medium-low heat until the apples soften, about 10 minutes. Add the cranberries and wine and simmer until the wine evaporates and the cranberries are tender, about 5 minutes. Stir in the salt and pepper. Let cool.
In a large, heavy sauté pan, cook the sausages over medium-high heat until browned and cooked through, breaking them up with a wooden spoon, about 8 minutes. Lightly coat an 8½-inch square baking dish with ½ tablespoon of butter. In a medium bowl, combine the apple mixture, sausage, chestnuts, and cornbread. Gently stir in the broth and ¾ cup of the Parmesan. Season with salt and pepper. Transfer to the baking dish and sprinkle with ¼ cup of Parmesan. Bake until the top is golden brown and the stuffing is heated through, about 45 minutes.