01 - Preheat oven to 350°F. Grease and line three 8-inch round cake pans with parchment paper.
02 - In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
03 - In a large bowl, beat butter and sugar with an electric mixer until light and fluffy, about 3 to 4 minutes.
04 - Add eggs to the butter mixture one at a time, beating well after each addition. Mix in vanilla extract.
05 - Gradually add the flour mixture and milk to the batter, beginning and ending with flour. Mix until just combined.
06 - Divide the batter evenly among the prepared pans and smooth the surfaces. Bake for 25 to 28 minutes, or until a toothpick inserted in the center comes out clean.
07 - Let cakes cool in pans for 10 minutes, then turn out onto wire racks to cool completely.
08 - Combine apples, brown sugar, cinnamon, nutmeg, lemon juice, and water in a saucepan. Cook over medium heat, stirring occasionally, for 10 to 12 minutes until apples are soft and mixture turns syrupy. Let cool completely.
09 - Beat cream cheese and butter together until smooth. Gradually add powdered sugar, then add maple syrup, vanilla, and a pinch of salt. Continue beating until fluffy and well combined.
10 - Place one cake layer on a serving plate. Spread with one third of the frosting and half the apple compote. Repeat with the second layer. Top with final cake layer and frost the top and sides. Decorate with remaining apple compote or drizzle with maple syrup if desired.
11 - Refrigerate the cake for 30 minutes before slicing to ensure clean layers.