In a medium saucepan, combine diced apples, brown sugar, cornstarch, cinnamon, and water. Heat until boiling, then simmer for 10 minutes until apples are tender and liquid thickens.

Preheat your oven to 350°F (175°C) and line a muffin pan with cupcake liners.

In a large bowl, whisk together the cake flour, baking powder, ground cinnamon, and salt.

In a separate bowl, beat softened unsalted butter with granulated sugar until light and fluffy. Add the eggs one at a time, mixing well, then blend in vanilla extract.

Gradually add dry ingredients to wet mixture, alternating with milk until just combined.

Spoon the batter into cupcake liners, filling each two-thirds full.

Bake for about 20 minutes or until a toothpick inserted comes out clean. Let cool in the pan for 5-10 minutes before transferring to a wire rack.

Beat together softened unsalted butter and cream cheese until smooth. Gradually add powdered sugar, ground cinnamon, and vanilla extract until fluffy.

Once cooled, scoop out the center of each cupcake and fill with cooled apple compote, then pipe frosting on top.