01 - Preheat oven to 350°F. Line an 8 x 8 inch square baking pan with parchment paper, leaving an overhang for lifting.
02 - In a medium mixing bowl, whisk together melted butter and granulated sugar until smooth. Add eggs, vanilla extract, and red food coloring; whisk until fully incorporated.
03 - Sift in the all-purpose flour, unsweetened cocoa powder, and salt. Gently fold with a spatula until just combined. Spread approximately three-fourths of the batter evenly into the prepared pan, reserving the remainder.
04 - In a separate bowl, beat cream cheese and sugar until creamy using an electric mixer or whisk. Add egg and vanilla extract, mixing until fully smooth.
05 - Carefully pour the cheesecake batter over the brownie layer and spread evenly. Drop spoonfuls of the reserved red velvet batter onto the cheesecake layer and gently swirl using a knife or skewer for a marbled pattern.
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.
07 - Allow to cool completely in the pan on a wire rack. Once cool, chill in the refrigerator for at least 1 hour before slicing and serving.