01 - Preheat oven to 350°F. Line an 8 x 8 inch square baking pan with parchment paper, allowing overhang for easy lifting.
02 - In a medium bowl, whisk melted butter with sugar until fully combined. Add eggs, vanilla extract, and red food coloring, then whisk until smooth.
03 - Sift in flour, cocoa powder, and salt. Fold gently with a spatula until just mixed. Spread approximately three-quarters of the batter evenly in the prepared pan and reserve the remaining batter.
04 - In a separate bowl, beat softened cream cheese and sugar until creamy. Add the egg and vanilla extract, mixing until a smooth batter forms.
05 - Pour the cheesecake batter evenly over the red velvet base in the pan.
06 - Dollop the reserved red velvet batter in small spoonfuls over the cheesecake layer. Gently swirl with a knife or skewer to create a marbled effect.
07 - Bake for 33 to 37 minutes, until the center is just set and a toothpick inserted comes out with a few moist crumbs.
08 - Allow to cool fully in the pan. Transfer to the refrigerator and chill for at least 1 hour before slicing and serving.