01 - Preheat oven to 350°F (175°C). Line an 8 x 8 inch square baking pan with parchment paper, leaving an overhang for easy removal.
02 - In a medium bowl, whisk together melted butter and granulated sugar until fully integrated. Add eggs, vanilla extract, and red food coloring, whisking until smooth.
03 - Sift in all-purpose flour, unsweetened cocoa powder, and salt. Gently fold with a spatula until just combined. Spread approximately three-quarters of the red velvet batter evenly into the prepared pan, reserving the remainder.
04 - In a separate bowl, beat softened cream cheese and granulated sugar using an electric mixer or whisk until creamy. Add the egg and vanilla extract, mixing until smooth and uniform.
05 - Carefully pour the cheesecake batter over the red velvet layer in the pan and gently smooth into an even layer.
06 - Dollop the reserved red velvet batter on top of the cheesecake layer. Using a knife or skewer, swirl gently to achieve a marbled appearance.
07 - Place the pan in the preheated oven and bake for 33 to 37 minutes, or until the center is set and a toothpick inserted comes out with a few moist crumbs.
08 - Allow to cool completely in the pan, then refrigerate for at least 1 hour before slicing and serving.