01 - Preheat oven to 350°F. Line an 8 x 8 inch square baking pan with parchment paper, leaving an overhang on the sides for effortless removal.
02 - In a medium bowl, whisk together melted butter and sugar until fully blended. Add eggs, vanilla extract, and red food coloring, whisking until homogeneous.
03 - Sift flour, cocoa powder, and salt into the wet mixture. Fold gently with a spatula until just combined. Spread three-quarters of the batter evenly into the prepared pan, reserving the remaining portion.
04 - In a separate bowl, beat softened cream cheese and sugar together with an electric mixer or whisk until smooth and creamy. Add egg and vanilla extract, mixing thoroughly until fully incorporated.
05 - Pour the cheesecake mixture over the red velvet layer and spread gently for an even surface. Distribute dollops of the reserved red velvet batter on top and create a marbled effect by swirling with a knife or skewer.
06 - Bake in the preheated oven for 33 to 37 minutes, or until the center is just set and a toothpick inserted in the middle emerges mostly clean with a few moist crumbs.
07 - Allow to cool completely in the pan. Transfer to the refrigerator and chill for at least 1 hour before slicing and serving for optimal texture.