Prepare the Red Velvet Cake Layer

1. Preheat Oven: Preheat your oven to 350°F (175°C). Grease and line the bottom of a 9-inch springform pan with parchment paper. This helps with easy removal later.
2. Mix Dry Ingredients: In a medium bowl, whisk together the flour, sugar, cocoa powder, baking soda, and salt until fully combined.
3. Combine Wet Ingredients: In a separate large bowl, whisk together the egg, vegetable oil, vanilla extract, vinegar, buttermilk, and red food coloring.
4. Combine Wet and Dry Ingredients: Gradually add the dry ingredients to the wet ingredients, mixing until smooth and well combined.
5. Bake the Cake: Pour the red velvet batter into the prepared pan and smooth the top. Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
6. Cool the Cake: Remove from the oven and allow the cake to cool in the pan for 10 minutes. Transfer to a wire rack to cool completely.

Prepare the Cheesecake Layer

1. Prepare the Cream Cheese Mixture: In a large bowl, beat the softened cream cheese with an electric mixer until smooth and creamy. Add the sugar and vanilla extract, and beat until well incorporated.
2. Add the Eggs: Add the eggs one at a time, beating well after each addition. Be sure not to overmix to prevent air bubbles in the cheesecake.
3. Add the Sour Cream and Flour: Mix in the sour cream and flour, beating just until combined. The mixture should be smooth and creamy without lumps.
4. Assemble the Cheesecake: Pour the cheesecake mixture over the cooled red velvet cake layer in the springform pan. Use a spatula to spread it evenly.
5. Bake the Cheesecake: Bake at 325°F (163°C) for 50-60 minutes, or until the edges are set but the center is still slightly wobbly. This will ensure a creamy, smooth cheesecake filling.
6. Cool the Cheesecake: Turn off the oven and let the cheesecake cool inside with the door slightly ajar for 1 hour. This helps prevent cracks from forming. Afterward, transfer to a wire rack and cool completely at room temperature.
7. Chill: Once cooled, cover the cheesecake and refrigerate for at least 2 hours, or preferably overnight, to let the flavors set and the cheesecake firm up.