In a large bowl, use an electric mixer to cream together the butter and sugar on medium-high speed until light and fluffy, about 2 minutes. Add the egg and vanilla extract; mix until well combined.
In a separate bowl, whisk together the flour, baking soda, baking powder, nutmeg, and salt.
Add half of the flour mixture to the butter mixture; mix on medium-low speed until just combined. Add the sour cream and mix to combine. Add the remaining flour mixture and mix just until combined.
Fold in the diced apples.
Transfer the batter to the prepared baking dish.
Sprinkle the cinnamon-sugar topping on top.
Bake for about 25 minutes, or until a toothpick inserted in the center comes out clean. Cool in the pan for at least 30 minutes, then lift the cake out of the pan with the overhanging parchment paper.