01 - Preheat oven to 350°F. Line an 8 x 8 inch square baking pan with parchment paper, leaving an overhang on the sides for easy removal.
02 - In a medium mixing bowl, whisk melted butter and granulated sugar until smooth. Incorporate eggs, vanilla extract, and red food coloring, whisking until thoroughly blended.
03 - Sift in all-purpose flour, unsweetened cocoa powder, and salt. Fold gently with a spatula until just combined. Spread three-quarters of the batter evenly into the prepared pan, reserving the remainder.
04 - In a separate bowl, beat softened cream cheese and granulated sugar until creamy and smooth. Add egg and vanilla extract, mixing to a homogenous consistency.
05 - Pour the cheesecake mixture over the red velvet base and gently spread evenly. Dollop reserved brownie batter over the cheesecake layer and swirl with a knife or skewer to create a marbled effect.
06 - 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.
07 - Allow to cool completely in the pan. Transfer pan to refrigerator and chill for at least one hour before slicing and serving.