Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set aside.
In a large bowl, beat the butter and sugar together until light and fluffy, about 3-4 minutes. Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
Gradually add the dry ingredients to the wet mixture, alternating with the sour cream, beginning and ending with the flour mixture. Mix until just combined. Fold in the chopped apples.
Pour the batter into the prepared cake pan and spread it evenly. Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Once cooled, dust with powdered sugar if desired. Slice and serve.