Preheat the 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, salt, cinnamon, and nutmeg. Set aside.
In a large bowl, beat the softened butter and granulated sugar together until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Add half of the dry ingredients to the butter mixture and mix until just combined.
Add the sour cream and mix until incorporated.
Add the remaining dry ingredients and mix until just combined, being careful not to overmix.
Fold in the diced fresh apples gently.
Pour the batter into the prepared cake pan and spread evenly.
Bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before serving.