01 - Preheat the oven to 350°F and 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 bowl, whisk together the melted butter and sugar until well incorporated. Add eggs, vanilla extract, and red food coloring, whisking until completely blended.
03 - Sift in the flour, unsweetened cocoa powder, and salt. Fold gently with a spatula until just combined. Spread three-quarters of the red velvet batter evenly in the prepared pan, reserving the remainder.
04 - In a separate bowl, beat the softened cream cheese with sugar until smooth and creamy. Add the egg and vanilla, mixing until the cheesecake batter is fully smooth.
05 - Pour the cheesecake mixture carefully over the red velvet layer and spread into an even layer with a spatula.
06 - Place dollops of the reserved red velvet batter on top. Swirl gently with a knife or skewer to create a marbled effect.
07 - Bake for 33 to 37 minutes, or until the center appears set and a toothpick inserted into the center emerges mostly clean with a few moist crumbs lingering.
08 - Allow brownies to cool completely in the pan, then refrigerate for at least 1 hour to firm before slicing and serving.