Melt the butter in a small saucepan over medium heat. Add the diced apple, brown sugar, and cinnamon. Cook for 5–7 minutes, stirring occasionally, until the apples are tender but still hold their shape.

Remove from heat and transfer the filling to a small bowl. Allow it to cool completely before using.

Preheat your oven to 350°F (175°C) and line the muffin tin with paper liners.

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

In a large bowl, use an electric mixer to beat the softened butter, granulated sugar, and brown sugar until light and fluffy (about 3 minutes).

Beat in the eggs one at a time, then mix in the vanilla extract.

With the mixer on low speed, alternate adding the flour mixture and the buttermilk to the batter, beginning and ending with the flour mixture.

Fill each cupcake liner about halfway with batter. Place 1 heaping teaspoon of the cooled apple filling directly in the center of the batter. Top with a small amount of the remaining batter, filling the liners about two-thirds full.

Bake for 20–22 minutes, or until a toothpick inserted into the cake part comes out clean.

Cool the cupcakes in the tin for 5 minutes before transferring them to a wire rack to cool completely.

In a large bowl, use an electric mixer to beat the softened cream cheese and butter until completely smooth.

Gradually beat in the powdered sugar, cinnamon, and vanilla extract until the frosting is light and fluffy.

Once the cupcakes are completely cool, pipe or spread the frosting onto each one. Garnish with a tiny sprinkle of cinnamon or a small piece of baked apple and serve.