Line a 9x13-inch baking pan with parchment paper or foil sprayed with nonstick cooking spray. Set aside.
Make the red velvet layer: In a medium bowl, whisk together flour, cocoa powder, baking soda, and salt. Set aside.
In a large bowl, cream together the butter and sugars until fluffy.
Add the egg, vanilla extract, and red coloring, and mix until combined.
Add the dry ingredients to the bowl with the butter mixture and mix until well combined.
Press the batter into the bottom of the prepared pan. Set aside.
Make the cheesecake layer: Use a stand mixer or an electric mixer to beat the cream cheese and sugar together until smooth. Add in the sour cream, eggs, and vanilla extract, and beat until the mixture is smooth and free of lumps.
Pour the cheesecake filling over the red velvet crust.
Bake in the preheated oven for 42–45 minutes, until the center is set. Remove from the oven, cool to room temperature, and then refrigerate for at least 2 hours.