01 - Preheat oven to 350°F. Line an 8 x 8 inch square baking pan with parchment paper, allowing an overhang for easy removal.
02 - In a medium mixing bowl, whisk melted butter and granulated sugar until smooth. Incorporate eggs, vanilla extract, and red food coloring, mixing until fully combined.
03 - Sift all-purpose flour, unsweetened cocoa powder, and salt together, then gently fold into the wet mixture with a spatula until just combined.
04 - Spread three-quarters of the red velvet batter evenly into the prepared baking pan, reserving the remaining batter for topping.
05 - In a clean bowl, beat softened cream cheese and granulated sugar together until creamy and smooth. Blend in the egg and vanilla extract until uniform.
06 - Pour cheesecake batter over the red velvet base, spreading into an even layer.
07 - Dollop the reserved red velvet batter over the cheesecake layer. Swirl gently using a knife or skewer to create a marbled effect.
08 - Bake for 33 to 37 minutes, or until the center sets and a toothpick inserted near the center comes out mostly clean with a few moist crumbs.
09 - Allow the dessert to cool completely in the pan. Refrigerate for at least 1 hour before slicing and serving for optimal texture.