01 - Preheat oven to 350°F (175°C). Line an 8 x 8 inch pan with parchment paper, leaving an overhang for lifting.
02 - In a medium bowl, whisk together melted butter and sugar until glossy. Incorporate eggs, vanilla extract, and red food coloring until smooth.
03 - Sift in all-purpose flour, cocoa powder, and salt. Fold gently with a spatula until just combined. Spread three-quarters of the red velvet batter evenly in prepared pan, reserving remaining batter.
04 - In a separate bowl, beat softened cream cheese with sugar until creamy. Blend in the egg and vanilla extract until smooth and homogenous.
05 - Pour cheesecake mixture over red velvet base, spreading gently. Dollop reserved red velvet batter over the top and create swirls with a knife or skewer for a marbled finish.
06 - Bake for 33 to 37 minutes until the center is set and a toothpick inserted emerges with a few moist crumbs.
07 - Allow pan to cool completely, then refrigerate for at least 1 hour before slicing and serving.