Instructions

For the cake

1. To make the brown butter, place 2 tablespoons of butter in a microwave-safe bowl and top with a microwave-safe plate. Microwave for 3 to 5 minutes. The butter will pop while browning. Check the butter, and if not browned enough, microwave again in 1 minute increments. While the brown butter is cooling, stir periodically to incorporate the caramelized bits of butter. Cool completely.
2. Heat the oven to 350° F.
3. Combine the butters and sugars in the bowl of a stand mixer fitted with the paddle attachment and cream together on medium-high for 2 to 3 minutes. Scrape down the sides of the bowl, add the eggs, and mix on medium-high for 2 to 3 minutes. Scrape down the sides of the bowl of the bowl once more.
4. Stream in the buttermilk, oil, and vanilla while the paddle swirls on low speed. Increase the speed to medium-high and paddle 5 to 6 minutes, until the mixture is practically white, twice the size of your original fluffy butter-and-sugar mixture, and completely homogenous. You’re basically forcing too much liquid into an already fatty mixture that doesn’t want to make room for it, so if it doesn’t look right after 6 minutes, keep mixing. Stop the mixer and scrape down the sides of the bowl.
5. On very low speed, add the cake flour, baking powder, and salt. Mix for 45 to 60 seconds, just until your batter comes together an any remnants of dry ingredients have been incorporated. Scrape down the sides of the bowl. Mix on low speed for another 45 seconds to ensure that any lumps of cake flour are incorporated.
6. Pam-spray cupcake pan and fill with cupcake liners. Fill liners 3/4 full. Bake for 20 to 25 minutes. The cakes will rise and puff, but will remain slightly buttery and dense. At 20 minutes, gently poke the edge of the cake with your finger: the cake should bounce back slightly and the center should no longer be jiggly. Leave the cakes in the oven for an extra 3 to 5 minutes if it doesn’t pass these tests.
7. Take the cakes out of the oven and cool on a wire rack or, in a pinch, in the fridge or freezer (don’t worry, it’s not cheating). The cooled cake can be stored in the fridge, wrapped in plastic wrap, for up to 5 days.

For the soak

1. Whisk together the cider, brown sugar, and cinnamon in a small bowl until the sugar is completely dissolved.

For the liquid cheesecake

1. Heat the oven to 300° F.
2. Put the cream cheese in the bowl of a stand mixer fitted with a paddle attachment and mix on low speed for 2 minutes. Scrape down the sides of the bowl with a spatula. Add the sugar and mix for 1 to 2 minutes, until the sugar has been completely incorporated. Scrape down the sides of the bowl.
3. Whisk together the cornstarch and salt in a medium bowl. Whisk in the milk in a slow, steady stream, then whisk in the egg until the slurry is homogenous.
4. With the mixer on medium-low speed, stream in the egg slurry. Paddle for 3 to 4 minutes, until the mixture is smooth and loose. Scrape down the sides of the bowl.
5. Line the bottom and sides of a 6×6 inch baking pan with plastic wrap [the idea of this scared me, so I used aluminum foil]. Poor the cheesecake batter into the pan, put the pan in the oven, and bake for 15 minutes. Gently shake the pan. The cheesecake should be firmer and more set toward the outer boundaries of the baking pan but still be jiggly and loose in the dead center. If the cheesecake is jiggly all over, give it 5 minutes more. And 5 minutes more if it needs it, but it’s never taken me more then 25 minutes to underbake one. If the cheesecake rises more than a ¼ inch or begins to brown, take it out of the oven immediately.
6. Cool the cheesecake completely, to finish the baking process and allow the cheesecake to set. The final product will resemble a cheesecake, but it will be pipeable and pliable enough to easily spread or smear, while still having body and volume. Once cool, the cheesecake can be stored in an airtight container in the fridge for up to 1 week.

For the apple pie filling

1. Fill a medium bowl halfway with cold tap water. Juice the lemon into it. Fish out and discard any seeds. You will use this lemon water to keep your apple pieces looking fresh and pert.
2. Peel the apples, then halve and quarter them. Put each apple quarter on its side and cut a small slice down the length of the apple to remove the seeds and core. Cut each apple quarter lengthwise into thirds and then crosswise into fourths, leaving you with 12 small pieces from every apple quarter. Transfer these pieces to the lemon water as you go.
3. When you’re ready to cook, drain the apples (discard the lemon water) and combine them in a medium pot with the butter, brown sugar, cinnamon, and salt. Slowly bring a boil over medium heat, using a spoon to gently stir the mixture as it heats up and the apples begin to release liquid. Reduce the heat and simmer the apples gently for 3 to 5 minutes. Be careful not to cook the apples so much that they turn into applesauce. [I had a lot of liquid left, so I fished out the apples and reduced the remaining liquid by half for about 5 to 6 minutes. It created a more caramel-y apple filling.]
4. Transfer to a container and put in the fridge to cool down. Once completely cooled, the filling can be stored in the fridge in an airtight container for up to 1 week; do not freeze.

For the pie crumb

1. Heat the oven to 350° F.
2. Combine the flour, sugar, and salt in the bowl of a stand mixer fitted with the paddle attachment and paddle on low speed until well mixed.
3. Add the butter and water and paddle on low speed until the mixture starts to come together in small clusters.
4. Spread the clusters on a parchment or Silpat lined sheet pan. Bake for 25 minutes, breaking them up occasionally. The crumbs should be golden brown and still slightly moist to the touch at that point; they will dry and harden as they cool.
5. Let the crumbs cool completely before using in a recipe or eating. Stored in an airtight container, the crumbs will keep fresh for 1 week at room temperature or 1 month in the fridge or freezer.

For the frosting

1. Combine the pie crumbs, milk, and salt in a blender, turn the speed to medium-high, and puree until smooth and homogenous. It will take 1 to 3 minutes (depending on the awesomeness of your blender). If the mixture does not catch on your blender blade, turn off the blender, take a small teaspoon, and scrape down the sides of the canister, remembering to scrape under the blade, then try again.
2. Combine the butter and confectioners’ sugar in the bowl of a stand mixer fitted with the paddle attachment and cream together on medium-high for 2 to 3 minutes, until fluffy and pale yellow. Scrape down the sides of the bowl with a spatula.
3. On low speed, paddle in the contents of the blender, After 1 minute, crank the speed up to medium-high and let her rip for another 2 minutes. Scrape down the sides of the bowl. If the mixture is not a uniform, very pale, barely tan color, give the bowl another scrape-down and another minute of high-speed paddling.
4. Use the frosting immediately, or store it in an airtight container in the fridge for up to 1 week.