01 - Preheat oven to 350°F. Line an 8 x 8 inch square baking pan with parchment paper, leaving an overhang for easy lifting.
02 - In a medium bowl, whisk melted butter and granulated sugar until smooth. Add eggs, vanilla extract, and red food coloring, whisking to incorporate.
03 - Sift in all-purpose flour, unsweetened cocoa powder, and salt. Fold gently with a spatula until just combined. Spread approximately three-quarters of this batter evenly into the prepared pan, reserving the remainder.
04 - In a separate bowl, beat softened cream cheese and granulated sugar until creamy. Add egg and vanilla extract, mixing until smooth and uniform.
05 - Pour cheesecake mixture over the red velvet batter in the pan and gently spread into an even layer.
06 - Dollop the reserved red velvet batter on top of the cheesecake layer. Use a knife or skewer to gently swirl the batters together, creating a marbled appearance.
07 - Bake for 33 to 37 minutes, or until the center is set and a toothpick inserted comes out mostly clean with a few moist crumbs.
08 - Allow to cool completely in the pan on a wire rack. Refrigerate for at least 1 hour before slicing and serving for best texture.