01 - Preheat oven to 350°F (175°C). Line an 8 x 8 inch square baking pan with parchment paper, allowing extra overhang for easy removal.
02 - In a medium bowl, whisk together melted butter and granulated sugar until the mixture is glossy. Add eggs, vanilla extract, and red food coloring, whisking until smooth.
03 - Sift in all-purpose flour, unsweetened cocoa powder, and salt. Gently fold with a spatula until just incorporated. Spread approximately three-quarters of the red velvet batter evenly in the prepared pan, reserving the remainder.
04 - In a separate bowl, beat softened cream cheese and granulated sugar using an electric mixer or whisk until creamy. Blend in the egg and vanilla extract, mixing until the batter is smooth.
05 - Carefully pour the cheesecake mixture over the red velvet base and spread into an even layer.
06 - Dollop the reserved red velvet batter on top of the cheesecake layer. Use a knife or skewer to gently swirl for a marbled effect.
07 - Bake for 33 to 37 minutes, or until the center is set and a toothpick inserted comes out mostly clean with a few moist crumbs.
08 - Let cool completely in the pan. Chill in the refrigerator for at least 1 hour prior to slicing and serving.