Apple Pie Layer Cake

Instructions

1. To make the cake, preheat the oven to 350ºF.  Butter and flour the edges of a quarter sheet pan. Line the bottom of the pan with parchment paper.  Set aside.
2. Combine the butter, browned butter and sugars in the bowl of a mixer fitted with the paddle attachment.  Beat together on medium-high speed until smooth, about 2-3 minutes.  Scrape down the sides of the bowl.  Add in the eggs and mix again on medium-high speed for 2-3 minutes.  Scrape down the sides of the bowl again.  With the mixer on low speed, pour in the buttermilk, oil and vanilla.  Increase the speed to medium-high and beat for 5-6 minutes, until the mixture is almost doubled in volume and nearly white.  Don't under mix this stage.
3. With the mixer on low speed, add in the cake flour, baking powder and salt.  Mix just until the batter comes together and no flour streaks remain.  Spread the batter in the prepared quarter sheet pan.  Bake for 30-35 minutes, rotating the pan once halfway through baking, until the cake is puffed and the center is no longer jiggly (the cake should bounce back when lightly poked with your finger.)  Transfer to a wire cooling rack and let cool completely.  The cooled cake can be wrapped well in plastic wrap and stored in the fridge for up to 5 days.
4. To make the soak, combine the cider, brown sugar, and cinnamon in a small bowl. Whisk together until the sugar is completely dissolved.  Set aside.
5. To make the liquid cheesecake, preheat the oven to 300ºF. Line a small loaf pan (8 1/2 x 5 1/2-inches) with parchment paper. Place the cream cheese in the bowl of an electric mixer and mix on low speed for 2 minutes. Scrape down the sides of the bowl, then add in the sugar and mix 1-2 minutes more.  Scrape down the sides of the bowl again.  In a small bowl, combine the cornstarch and salt, then whisk in the milk and then the egg until smooth.  With the mixer on medium-low speed, pour in the egg mixture.  Mix for 3-4 minutes, until smooth.
6. Transfer the mixture to the prepared pan and spread in an even layer.  Bake 15-20 minutes. Gently shake the pan. You want the cheesecake to be firmer toward the outer edges but still jiggly in the center. Continue to bake as needed until this texture is achieved. Do not overbake – you want this to be under baked! Transfer to a wire rack to cool completely.
7. To make the pie crumb, heat the oven to 350ºF.  Combine the flour, sugar, and salt in the bowl of a stand mixer. Mix on low speed for a minute to combine.  Add in the butter and water and continue to mix on low speed until the mixture comes together in small clusters. Spread the clusters out on a lined baking sheet and bake for 25 minutes, stirring to break them up occasionally. They should be golden brown and still slightly moist to the touch. Transfer the pan to a wire rack. The crumbs will dry and harden as they cool. (You will use half of these as the pie crumb, and half to make the pie crumb frosting.) 
8. Peel and core the apples, then dice.  Combine them in a medium saucepan or skillet with the butter, brown sugar, cinnamon and salt.  Bring the mixture to a boil over medium heat, gently stirring as it heats up and the apples begin to release their liquid.  Lower the heat and let simmer for 3-5 minutes, until the apples have softened some but are not easily crushed into applesauce. Let cool.
9. To make the pie crumb frosting, combine half of the pie crumb you made above in a blender with the milk and salt. Purée until smooth and completely combined.  Combine the butter and confectioners’ sugar in the bowl of a mixer. Beat together on medium-high speed until fluffy and pale yellow, about 2-3 minutes.  Scrape down the sides of the bowl.  With the mixer on low speed, add in the pie crumb puree.  Increase the mixer speed to medium-high and beat for 2 more minutes. 
10. To assemble the cake, invert the cake from the sheet pan onto a work surface. Use a 6-inch cake ring to cut out 2 circles from the cake (these will be the top two layers.) Wipe off the cake ring and place it in the center of a sheet pan lined with clean parchment or a silpat. Use a strip of acetate to line the inside of the cake ring.  Use scraps from the leftover cake to place in the ring and push together in a flat, even layer.  Dip a pastry brush in the apple cider soak and give the layer of cake a healthy bath of half of the soak.  Use the back of a spoon to spread half of the liquid cheesecake in an even layer over the cake.  Sprinkle a third of the remaining pie crumbs over the liquid cheesecake, pressing down gently to anchor them in place.  Use the back of a spoon to spread one half of the apple pie filling as evenly as possible over the crumb mixture.
11. Gently tuck a second strip of acetate between the cake ring and the top 1/4-inch of the first strip of acetate.  Set a cake round on top of the frosting, and repeat the layering process once more (apple cider soak, remaining liquid cheesecake, half of the remaining pie crumb, remaining apple pie filling.)  Place the remaining cake layer on top of the apple pie filling. Cover the top of the cake with half of the pie crumb frosting.  Sprinkle the remaining pie crumbs on top for garnish.
12. Transfer the assembled cake to the freezer and freeze for a minimum of 12 hours to set the cake and the filling. The cake will keep in the freezer for up to 1 month. At least 3 hours before you are ready to serve, remove the pan from the freezer, pop the cake out of the cake ring, and peel away the acetate layers.  Transfer to a cake platter and defrost for at least 3 hours before slicing and serving.