Preheat your oven to 350°F and grease a 9-inch cake pan.

In a medium-sized bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.

In a separate large bowl, beat together the butter and sugar until light and fluffy. Then, add the eggs and vanilla extract one at a time, mixing well after each addition.

Gradually add the dry ingredients to the wet mixture, alternating with the buttermilk and mixing just until everything is well combined.

Fold in the chopped apples and walnuts.

Pour the batter into the prepared pan and smooth out the top with a spatula.

Bake for 50-55 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 before transferring it to a wire rack to cool completely.

Slice and serve!