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.
In 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 and egg yolk, 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 for 40 minutes.
Remove from oven and allow to cool for at least an hour before transferring to fridge to cool for at least 6 hours.
Preheat oven to 350F and prepare two 9" cake pans by greasing and lightly flouring
In saucepan over medium heat, combine 2 cups milk and dark chocolate, stirring until chocolate is completely melted.
Increase heat to medium-high, stir constantly until mixture begins to bubble and stir in cocoa powder. Remove from heat and set aside.
In KitchenAid, combine canola oil and sugars, beat on medium speed for about 1 minute, until ingredients are well-combined.
Add eggs, one at a time, beating well after each addition, and vanilla.
In a separate bowl, combine flour, baking powder, baking soda, and salt.
With mixer on low-medium speed, gradually stir in flour mixture to butter/sugar mixture, pausing to scrape down the sides of the bowl occasionally.
Pour the cocoa/dark chocolate liquid into the mixer and beat on medium speed until combined.
Scrape down sides of bowl and add 3 Tbsp milk, stir on medium speed again so all ingredients are combined.
Evenly divide batter between cake pans.
Bake on 350F for 20 minutes (toothpick inserted into middle of cupcake should come out clean).
Allow to cool completely before assembling cake (it may be helpful to place cakes in freezer for about 15 minutes before frosting to eliminate crumbs mixing into the icing)
Frosting and assembly
Cream together cream cheese and butter on medium speed of KitchenAid mixer (or with electric hand mixer)
Add vanilla and cocoa powder and stir. Gradually stir in sugar, pausing periodically to scrape down sides of bowl with a spatula.
Add heavy cream and gradually increase speed to medium-high speed, then all the way to high-speed. Pause once to scrape down sides and bottom of bowl so all ingredients are incorporated.
Once cake and cheesecake have both cooled completely, carefully transfer one 9" chocolate cake round to cake stand/serving platter and layer with 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 on top of first chocolate cake layer and spread frosting over top of cheesecake..
Place second chocolate cake layer on top of cheesecake layer