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 lifting.
02 - In a medium bowl, whisk melted butter and granulated sugar until completely smooth. Incorporate eggs, vanilla extract, and red food coloring, whisking until well-combined.
03 - Sift flour, cocoa powder, and salt into the butter mixture. Fold gently with a spatula until just incorporated. Spread about three-quarters of the batter evenly into the prepared pan, reserving the rest.
04 - In a separate bowl, beat softened cream cheese and granulated sugar with an electric mixer or whisk until creamy. Add egg and vanilla extract, blending until smooth and homogeneous.
05 - Pour cheesecake mixture evenly over the red velvet brownie base. Dollop reserved red velvet batter on top and use a knife or skewer to swirl, creating a marbled pattern.
06 - Bake for 33 to 37 minutes or until the center is set and a toothpick inserted in the center yields mostly clean results with a few moist crumbs attached.
07 - Allow baked confection to cool completely in the pan, then refrigerate for at least 1 hour before slicing for optimal texture.