Preheat the oven to 350°F (175°C). Lightly grease a 9x13 inch baking pan or line it with parchment paper for easier removal.
In a large mixing bowl, combine the melted butter and granulated sugar. Mix until well combined.
Add the vanilla extract and eggs to the mixture, one at a time, stirring well after each addition.
In another bowl, sift together the flour, cocoa powder, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, stirring until just combined.
Mix in the red food coloring until the batter is uniformly colored and smooth.
In a separate bowl, beat together the softened cream cheese, powdered sugar, egg, and vanilla extract for the cheesecake layer until creamy and smooth.
Pour half of the red velvet batter into the prepared baking pan and spread it evenly.
Carefully spoon dollops of the cream cheese mixture over the red velvet layer. Use a knife to swirl the two mixtures together to create a marbled effect.
Pour the remaining red velvet batter on top and gently spread to cover the cheesecake layer.
Bake in the preheated oven for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Allow the brownies to cool in the pan before slicing them into squares.
Notes
Serve the brownies on a decorative platter. Dust with extra powdered sugar for a charming finish and add fresh raspberries on the side for a pop of color.