01 - Preheat the oven to 350°F (175°C). Line an 8 x 8 inch square baking pan with parchment paper, allowing some overhang for easy removal.
02 - In a medium mixing bowl, whisk together melted butter and sugar until smooth. Add eggs, vanilla extract, and red food coloring, blending until fully combined.
03 - Sift in all-purpose flour, unsweetened cocoa powder, and salt. Gently fold the mixture with a spatula until just incorporated. Spread approximately three-quarters of the red velvet batter evenly into the lined pan, reserving the remainder.
04 - In a separate bowl, beat the softened cream cheese and granulated sugar with an electric mixer until creamy. Incorporate the egg and vanilla extract, mixing until the batter is smooth.
05 - Pour the cheesecake mixture over the red velvet base and spread into an even layer.
06 - Drop spoonfuls of the reserved red velvet batter on top of the cheesecake layer. Using a knife or skewer, gently swirl to create a marbled effect.
07 - Bake in the preheated oven 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 a minimum of 1 hour before slicing and serving.