01 - Preheat oven to 350°F. Line an 8 x 8 inch baking pan with parchment paper, allowing for an overhang to facilitate removal.
02 - In a medium mixing bowl, whisk together melted butter and sugar until smooth. Incorporate eggs, vanilla extract, and red food coloring, whisking until fully integrated.
03 - Sift flour, unsweetened cocoa powder, and salt over the wet ingredients. Gently fold using a spatula just until combined. Spread 3/4 of the red velvet batter evenly in the prepared pan, reserving the remainder.
04 - In a separate bowl, beat softened cream cheese with sugar until creamy. Add egg and vanilla extract, mixing until the batter is smooth and homogeneous.
05 - Carefully pour the cheesecake mixture over the red velvet brownie layer, spreading evenly. Dollop the reserved red velvet batter over the surface and use a knife or skewer to gently swirl for a marbled appearance.
06 - Bake for 33 to 37 minutes, or until the center is set and a toothpick inserted in the center comes out mostly clean with a few moist crumbs attached.
07 - Allow to cool completely in the pan, then refrigerate for at least 1 hour to set layers before slicing and serving.