Begin by preheating the oven to 325°. Next, take a 9-in. springform pan and line the bottom with parchment paper, then grease the paper.
In a large mixing bowl, beat the cream cheese and sugar together until the mixture becomes smooth. Afterwards, add the sour cream, flour and vanilla, then beat everything together. Gradually add in the eggs and beat on low speed until the ingredients are just blended. Pour the mixture into the prepared pan and place it on a baking sheet.
Bake the mixture until the center is set, which should take around 40-50 minutes. After baking, let it cool on a wire rack for about 10 minutes. Loosen the sides from the pan using a knife, then let it cool for an additional hour. Once the cheesecake is completely cooled, cover it and refrigerate until it's time to assemble the final product.
For the cake, increase the oven temperature to 350°. Take two 9-in. round baking pans and grease them, then line the bottoms of each pan with parchment paper.
In a separate large mixing bowl, beat the sugar, oil, buttermilk, eggs, food coloring, vinegar and vanilla together until they're well blended. In another bowl, whisk the flour, cocoa, baking soda and salt together, then gradually beat the mixture into the sugar blend.
Pour the mixture into the prepared pans and bake it until a toothpick inserted in the center comes out clean. This should take about 30-35 minutes. Let the cake cool in the pans for about 10 minutes before removing them and the parchment paper. Allow the cake to cool completely.
To make the frosting, take a large mixing bowl and beat the cream cheese, butter and vanilla until the mixture is smooth. Gradually beat in enough confectioners' sugar until the desired consistency is reached.
Place one cake layer on a serving plate, then spread 1 cup of frosting over it. Carefully place the cheesecake over the frosting, then spread another 1 cup of frosting over the cheesecake. Place the remaining cake layer on top, then frost the top and sides of the cake with the remaining frosting. Refrigerate the cake overnight before serving.