Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans. In a large mixing bowl, cream together the butter and sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.

In a separate bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt. Gradually add the dry ingredients to the wet mixture, alternating with milk, until just combined. Fold in the chopped apples.

Divide the batter evenly between the prepared pans. Smooth the tops with a spatula. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Allow cakes to cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.

In a large bowl, beat the softened butter until creamy. Gradually add the powdered sugar, one cup at a time, beating well after each addition. Mix in the cinnamon and vanilla extract. Add milk, one tablespoon at a time, until the frosting reaches the desired consistency.

Once the cakes are completely cool, place one layer on a serving plate. Spread a generous amount of cinnamon buttercream over the top. Place the second layer on top and spread buttercream over the top and sides of the cake. Decorate as desired.

Wrap leftover cake tightly in plastic wrap or place it in an airtight container. Store at room temperature for up to two days, or refrigerate for up to five days. For longer storage, freeze individual slices wrapped in plastic wrap and placed in a freezer-safe container.