Preheat oven to 350°F (175°C) and line an 8x8 inch baking pan with parchment paper.
In a mixing bowl, combine melted butter, cocoa powder, and red food coloring. Stir until well blended.
Add sugar, vanilla extract, salt, and egg. Mix well.
Fold in flour until just combined and set aside 2-3 tablespoons of the batter for swirling.
Pour the remaining batter into the prepared pan and smooth the top.
In a separate bowl, mix softened cream cheese, 2 tablespoons sugar, and 1/4 teaspoon vanilla until smooth.
Drop spoonfuls of the cheesecake mixture over the brownie batter, then spoon reserved red velvet batter on top.
Use a toothpick or knife to gently swirl the batters together.
Bake for 25-30 minutes or until a toothpick comes out mostly clean with a few moist crumbs.
Cool completely before slicing into squares.