Preheat oven: Set oven to 350°F. Line a 12-cup muffin tin with paper liners.
Mix dry ingredients: In a medium bowl, whisk together 1 1/4 cups flour, 1 teaspoon baking powder, 1 teaspoon cinnamon, and 1/2 teaspoon salt. Set aside.
Cream butter and sugar: In a stand mixer (or with a hand mixer), beat 4 tablespoons butter and 3/4 cup sugar until light and fluffy, about 2 minutes.
Add egg and vanilla: Mix in 1 large egg and 1/2 teaspoon vanilla extract until smooth.
Combine batter: Add the dry ingredients to the wet ingredients, mixing until just combined. Pour in 1/4 cup buttermilk and mix until incorporated. Gently fold in 1 1/2 cups chopped apple.
Bake: Spoon batter evenly into the prepared muffin cups. Bake for 22–25 minutes, or until a toothpick inserted into the center comes out clean. Cool cupcakes completely before frosting.
Make frosting: In a large bowl, beat 1 cup butter and 4 ounces cream cheese until creamy. Mix in 2 1/2 teaspoons vanilla extract. Gradually beat in 4 cups powdered sugar and 1 1/2 teaspoons cinnamon until fluffy.
Frost & drizzle: Pipe or spread frosting on cooled cupcakes. Drizzle with caramel sauce just before serving.