Preheat oven to 350 degrees. Butter a 13-by-9-inch baking dish; set aside. Bring a large pot of salted water to a boil. Add noodles; cook until al dente according to package instructions, about 6 minutes. Drain noodles; return to pot. Set aside.
Put eggs and sour cream into the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until combined. Mix in 3/4 cup sugar, 3/4 cup butter, and the cream cheese. Set aside.
Heat 2 tablespoons butter in a large skillet over medium heat. Stir in 2 tablespoons sugar, the cinnamon, and nutmeg. Add apples; gently toss to coat. Cook, tossing occasionally, until soft and caramelized, 10 to 12 minutes. Stir apples into egg mixture; pour over noodles. Toss gently to combine. Pour into prepared dish. Drizzle remaining 2 tablespoons butter over noodles; sprinkle with remaining 2 tablespoons sugar.
Bake until set and top is golden brown, about 30 minutes. Transfer to a wire rack; let stand 15 minutes before serving.