Preheat an oven to 350 degrees F (175 degrees C). Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once the water is boiling, stir in the egg noodles, and return to a boil. Cook the pasta uncovered, stirring occasionally, until the pasta has cooked through, but is still firm to the bite, about 5 minutes. Drain well in a colander set in the sink. Place a large skillet over medium-high heat; cook the sausages until completely cooked, 5 to 7 minutes. Stir together the sugar and cinnamon in a small bowl. Pour the melted butter into the bottom of a 9x13 inch baking dish; layer half of the cooked egg noodles into the bottom of the dish; top with half of the sausage slices and half of the apple slices; sprinkle about half of the cinnamon-sugar mix over the dish. Repeat layers with remaining noodles, sausage, apples, and cinnamon-sugar. Dot with the butter pieces. Bake in the preheated oven until the apples are soft, 30 to 45 minutes.