Preheat the oven to 350 degrees Fahrenheit (175 degrees Celsius). Prepare an 8-inch springform pan by lining the bottom with parchment paper and spraying the sides with non-stick spray. Set aside.
For the cheesecake layer: In the bowl of a stand mixer fitted with a paddle attachment, cream the softened cream cheese for 5-6 minutes until light and fluffy. Scrape the sides and bottom of the bowl.
With the mixer on low speed, gradually add the sugar and flour. Once combined, increase the speed to medium and mix for an additional 2-3 minutes.
Reduce the mixer to low speed and add the eggs one at a time, scraping down the sides of the bowl as needed. Mix in the vanilla extract.
Pour in the heavy cream and mix on low speed, gradually increasing to high speed for 2-3 minutes until well combined.
Pour the cheesecake batter into the prepared pan and gently tap to release any air bubbles. Bake for 10 minutes at 350°F, then reduce the heat to 200°F and bake for an additional 55-60 minutes until the edges are set and the center slightly jiggles.
Turn off the oven and let the cheesecake cool for 15 minutes before removing. Allow it to cool completely on a wire rack, then refrigerate for at least 2 hours or overnight.
For the cake: Prepare two 8-inch cake pans by greasing with vegetable shortening and flour. Set aside.
In the bowl of a stand mixer with a paddle attachment, cream together the softened butter, brown sugar, and granulated sugar on high speed for 3-4 minutes until light and fluffy.
Gradually add the eggs one at a time, scraping down the sides of the bowl as needed.
Add the flour, baking powder, baking soda, salt, and cinnamon. Mix until just combined.
Fold in the grated carrots until evenly distributed. Divide the batter evenly between the prepared pans and bake for 20-25 minutes until a toothpick inserted into the center comes out clean. Let cool on a wire rack.
For the frosting: In the bowl of a stand mixer fitted with a paddle attachment, cream together the softened cream cheese and butter for 2-3 minutes until light and fluffy. Mix in the vanilla extract.
Gradually add the powdered sugar, scraping down the sides of the bowl as needed. Add the heavy whipping cream and mix on high speed for 2-3 minutes until smooth and creamy.
To assemble: Place one cake layer on a cake stand or serving plate. Spread a generous amount of frosting on top.
Carefully remove the springform pan from the cheesecake and place it face-down on top of the frosted cake layer. Remove the bottom of the pan and parchment paper. Spread frosting on top of the cheesecake layer.
Place the second cake layer on top and frost the entire cake with the remaining frosting. Smooth the frosting with a spatula.
Optionally, top the cake with crushed pecans.
Refrigerate the cake, preferably in an airtight container or covered with plastic wrap, until ready to serve.