Pre-heat your oven to 350 degrees.
Prepare an 8x8 pan by lining it with parchment paper and spraying it with non-stick spray. (if you don't have parchment, just spray very well.)
Add the butter and the baking chocolate to a small bowl and melt together in the microwave. Start with 30 seconds, then stir and continue in 30 second intervals until melted. Set aside to cool.
In a larger bowl, add in the sugar, eggs, vanilla extract, red coloring. Beat together with an electric mixer or whisk.
Add in the chocolate/butter mixture and beat again until combined.
Sprinkle the flour over the batter and use a spatula to incorporate into the batter.
Pour the batter into your prepared pan and set aside while you make the cheesecake mixture.
Add all of the cheesecake ingredients (cream cheese, egg, sugar, and vanilla) to a small bowl and beat until combined.
Spoon the mixture into dollops all over the red velvet batter.
Use a spoon or knife to swirl the cheesecake mixture into the red velvet batter.
Bake in the oven for 35-40 minutes or until a toothpick comes out clean.
Allow to cool in the pan then slice and serve!