Prepare cheesecake at least 4-6 hours before you wish to assemble the cake!
Preheat oven to 350F (175C)
Line 9" springform pan with parchment paper (remove the bottom, cover with a square of parchment paper and return rim (parchment paper will be sticking out the sides). This helps to make the cheesecake more easily transferable to the center of the other cake.
Using an electric mixer, beat together softened cream cheese, sugar and vanilla, scraping down the sides with a spatula occasionally to ensure it is mixed well. (beat on medium-speed about 1-2 minutes, scraping down side occasionally, it should be creamy and well-mixed)
Add sour cream, mix well, stopping once to scrape down the sides before mixing again.
Add eggs, one at a time, beating until just mixed after each addition (and scraping down the sides after each addition)
Pour cheesecake batter into prepared springform pan.
Bake on 350F (175C) for 40 minutes.
Remove from oven and allow to cool to room temperature before transferring to fridge to cool for at least 4-6 hours.
Preheat oven to 350F (175C) and grease and flour two 9-inch round pans.
In large bowl or KitchenAid mixer whisk together flour, sugars, baking powder, baking soda, salt, cinnamon and nutmeg.
Stir in canola oil. Add eggs, one at a time, pausing to scrape down sides of the bowl after each addition.
Stir in vanilla extract.
Stir in carrots and nuts (if using).
Evenly divide carrot cake batter between prepared baking pans and bake on 350F (175C) for 30-35 minutes (toothpick inserted in center should come out mostly clean with only few crumbs).
Allow to cool in the pans for 10 minutes, then run a knife around the edge and invert onto cooling rack to cool completely.
Frosting & Assembly
In KitchenAid or with hand mixer, cream together butter and cream cheese. Stir in vanilla extract.
Gradually, carefully, stir in powdered sugar until completely combined (be sure to scrape down sides of bowl to ensure ingredients are well-combined).
Add heavy cream (start with just 1 Tablespoon, only adding the second if needed) and beat on medium-high speed for 30 seconds. Scrape down sides of bowl and then beat again for 15 more seconds.
Once cake and cheesecake have both cooled completely, carefully transfer one 9" carrot cake layer to cake stand/serving platter and layer the top with the cream cheese frosting.
Run a knife around the inside edge of the springform pan to loosen the cheesecake and remove the sides of the pan. Carefully place the cheesecake on the prepared carrot cake layer (you may need to trim the sides of the cheesecake with a sharp knife if it isn't exactly the same size as your cake layer). Layer the top of the cheesecake with the frosting.
Place second carrot cake layer on top of iced cheesecake layer.
Apply icing to the top and around the sides of the cake. You may wholly cover the cake or run a straight edge spatula against the surface of the cake for a semi-naked look.
Serve. Keep uneaten cake in the refrigerator.
This cream cheese frosting is a very smooth one ideal for naked frosting cover for the cake. For a sturdier frosting that covers the whole cake, please check out my standalone cream cheese frosting recipe.