Cheesecake Layer: Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan and line the bottom with parchment paper. Using a stand mixer, cream the cream cheese until smooth. Gradually add sugar and flour, then mix in vanilla and cinnamon. Add the heavy cream, then add eggs one at a time, mixing until fully incorporated. Pour the batter into the prepared pan and tap gently on the counter. Bake at 350°F for 10 minutes, reduce to 200°F, and bake for 30-35 minutes until the center jiggles. Cool in the oven for 15 minutes with the door slightly open. Refrigerate overnight.
Spice Cake Layer: Preheat the oven to 350°F (175°C) and grease a 9-inch cake pan. In a medium bowl, whisk together the dry ingredients. In a stand mixer, cream the butter and brown sugar until fluffy. Add the oil, egg, and vanilla, and mix well. Gradually add the dry ingredients, alternating with milk, and mix until smooth. Pour the batter into the prepared pan and bake for 15-17 minutes until a toothpick comes out clean. Let cool and refrigerate overnight.
Buttercream Frosting: In a stand mixer, beat softened butter on high speed for 1-2 minutes until smooth. Gradually add powdered sugar, vanilla, cinnamon, and mix until well combined. Add heavy cream and mix on high for 1-2 minutes until fluffy.
Assembling the Piecaken: Trim the cheesecake, cake, and pumpkin pie layers to the same size. Place the cheesecake layer face down on a cake stand, frost with ¾ cup buttercream. Add the cake layer on top, then frost with another ¾ cup buttercream. Trim the pumpkin pie to fit and place it as the top layer. Frost the entire piecaken with the remaining buttercream. Refrigerate for 20-30 minutes to set. Optionally, pipe additional frosting around the edges.
