Combine the apples, brown sugar, cinnamon, nutmeg, cornstarch, lemon juice, and water in a saucepan. Cook over medium heat, stirring often, for 10 to 12 minutes until thickened. Cool completely.
Preheat oven to 350 degrees F. Grease and flour three cake pans and line the bottoms with parchment rounds.
Whisk the cake flour, baking powder, cinnamon, nutmeg, and salt in a medium bowl.
In a stand mixer, beat the butter and sugar on medium speed for 3 minutes until light and fluffy.
Add eggs one at a time, mixing until just combined after each.
Mix in the vanilla extract.
With the mixer on low, add the flour mixture in three additions, alternating with the buttermilk in two additions, starting and ending with flour.
Divide the batter among the three pans and bake for 26 to 30 minutes, until a toothpick comes out clean.
Cool in the pans for 10 minutes, then transfer to a wire rack to cool completely before frosting.
Beat the cream cheese and butter until smooth. Add powdered sugar gradually, then mix in cinnamon, vanilla, and salt until fluffy.
Pipe a thick ring of frosting around the edge of the first layer, spread the apple filling inside the ring, and repeat with the second layer before adding the third.
Apply a thin crumb coat, refrigerate for 20 minutes, then apply the final coat of frosting.
Slice and serve, or refrigerate until ready to serve.