For the potatoes: Bring a pot of water with the cubed potatoes to a boil and boil until tender, 15 to 20 minutes. Drain. Heat the milk and butter in a pot, then add it to the cooked potatoes and mash until smooth. Mix in the salt and pepper. Set aside.
For the meat and cabbage: Meanwhile, heat the oil in a large saucepan over medium-high heat. Add the beef and sausage and cook, stirring and breaking it up with a wooden spoon, until cooked through, 5 to 7 minutes. Remove the meat with a slotted spoon and set aside. Add the cabbage and cook, stirring occasionally, until softened, about 7 minutes, then add the meat back in and stir. Set aside.
Preheat the oven to 375 degrees F.
For the cheese sauce: Melt the butter in a heavy-bottomed saucepan. Stir in the flour and cook, stirring constantly, until the paste bubbles a bit but does not brown, 2 to 3 minutes. Whisk in the hot milk, continuing to stir as the sauce thickens, and bring it to a boil. Add 1 teaspoon each salt and pepper, then lower the heat and add the Cheddar. Cook until a smooth sauce is obtained. Add additional salt and pepper if needed.
For the assembly: Spray a 9-by-13-inch baking dish with some cooking spray. Spoon a thin layer of the cheese sauce on the bottom of the dish, then place 4 of the noodles on the sauce. Top with a third of the meat-cabbage mixture, a third of the potatoes and a third of the cheese sauce. Layer in another 4 noodles, another third of the meat-cabbage mixture, potatoes and cheese sauce and sprinkle in half of the Parmesan. Repeat the layers one more time, then top the final layer with the remaining Parmesan. Bake until golden, 30 to 45 minutes. Sprinkle with chopped parsley and serve.