Prepare the cupcakes:
Preheat your oven to 350°F (176°C) and line a cupcake pan with cupcake liners.
In a medium bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and salt. Set aside.
In a large mixing bowl, beat together the butter, vegetable oil, sugar, and brown sugar for about 3-4 minutes, until light and fluffy. Be sure to cream well.
Mix in the vanilla extract and sour cream until fully combined.
Add the eggs one at a time, beating well after each addition and scraping down the sides of the bowl as needed.
Add half of the dry ingredients to the batter and mix until combined.
Gradually add the milk and mix until well incorporated (the batter may look curdled, but that’s fine).
Mix in the remaining dry ingredients just until combined and smooth, taking care not to overmix.
Gently fold in the finely chopped apples.
Fill the cupcake liners about ¾ full and bake for 15-18 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cupcakes from the oven and allow them to cool on a wire rack.
Make the caramel buttercream:
In a large mixing bowl, beat the room temperature butter until smooth and creamy.
Add half of the powdered sugar and mix until fully combined.
Add 4 tablespoons of caramel sauce and a pinch of cinnamon, mixing until smooth.
Add the remaining powdered sugar and mix until creamy and well combined. Add more caramel sauce as needed to reach the desired taste and consistency.
Assemble the cupcakes:
Once the cupcakes have cooled completely, pipe the caramel buttercream on top of each cupcake.
Drizzle additional caramel sauce over the frosting and top with an apple slice for decoration.
Storage:
These cupcakes are best enjoyed fresh but can be stored covered in the refrigerator for 2-3 days. Bring to room temperature before serving.