In a small pot, combine the diced apples, brown sugar, cornstarch, ground cinnamon, and water. Cook over medium heat for about 10 minutes, or until the apples are tender.

Preheat your oven to 350°F (175°C) and prepare a muffin pan by lining it with parchment cupcake liners.

In a small bowl, sift together the cake flour, baking powder, salt, and one teaspoon of ground cinnamon. Set aside.

In a large mixing bowl, beat softened butter until creamy. Gradually add granulated sugar, then eggs, mixing well after each addition. Stir in vanilla extract.

Slowly add dry ingredients to the wet mixture, alternating with milk. Mix gently until just combined.

Carefully fill the lined muffin cups with batter until they are about two-thirds full.

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

In a mixing bowl, beat together the softened butter, cream cheese, powdered sugar, cinnamon, and vanilla extract until smooth.

Once cupcakes are cooled, scoop out a small portion from the center of each and fill with cooled apple compote. Pipe frosting on top.