In a small saucepan, combine diced apples, brown sugar, cornstarch, cinnamon, and water. Cover and bring to a boil over medium-high heat. Uncover and cook until apples are tender and liquid has mostly evaporated, stirring frequently. Add extra water if needed to prevent sticking. Cool completely.
Preheat oven to 350°F. Line a 12-cup muffin pan with cupcake liners.
In a small bowl, whisk together cake flour, baking powder, cinnamon, and salt. Set aside.
In a large bowl, beat softened butter with a hand mixer until creamy. Add sugar and beat until light and fluffy. Add eggs one at a time, mixing well after each addition. Mix in vanilla extract.
Sift in half the dry ingredients and mix on low speed until barely combined. Add half the milk and mix gently. Repeat with remaining dry ingredients and milk, mixing until smooth.
Fill cupcake liners about 2/3 full with batter. Bake for 20 minutes or until a toothpick inserted into the center comes out clean. Cool in the pan for 5–10 minutes, then transfer to a wire rack to cool completely.
To make the frosting, beat softened butter until creamy. Add cream cheese, powdered sugar, cinnamon, and vanilla extract. Beat until smooth and fluffy. Transfer frosting to a piping bag fitted with your desired piping tips.
Use a small spoon or melon baller to scoop out the center of each cupcake halfway down. Fill each cupcake with apple compote. Spoon a little extra compote on top, leaving a border around the edge.
Pipe frosting decoratively over the cupcakes using ribbon and star piping tips if desired. Serve and enjoy.