01 - Preheat oven to 350°F. Line an 8 x 8 inch square baking pan with parchment paper, leaving an overhang on two sides for easy removal.
02 - In a medium bowl, whisk together the melted butter and granulated sugar until smooth. Add eggs, vanilla extract, and red food coloring; whisk until evenly combined.
03 - Sift flour, cocoa powder, and salt into the wet mixture. Gently fold together with a spatula until just combined. Do not overmix.
04 - Spread approximately three-quarters of the red velvet batter evenly into the prepared baking pan, reserving the remaining batter.
05 - In a separate bowl, beat softened cream cheese and sugar together until smooth and creamy. Add egg and vanilla; mix until fully incorporated.
06 - Carefully pour the cheesecake mixture over the red velvet base, using a spatula to spread evenly to the edges.
07 - Dollop reserved red velvet batter over the cheesecake layer. Using a knife or skewer, gently swirl the batters to produce a marbled effect.
08 - Bake for 33 to 37 minutes, or until the center is set and a toothpick inserted comes out with a few moist crumbs attached.
09 - Allow to cool completely in the pan. Transfer to the refrigerator and chill for at least 1 hour before slicing into squares.