Preheat the oven to 350ºF.
Line an 8×8-inch baking pan with parchment paper and spray with non-stick cooking spray. Set aside.
In a large mixing bowl, combine the melted butter together with the sugar, cocoa powder, vanilla, food coloring and salt, stirring to combine with a whisk. Then stir in the white vinegar.
In a small bowl, whisk together the eggs, and then stir them into the red velvet brownie batter. Fold or whisk in the flour until just combined, then pour the ¾ of the batter into the prepared pan, reserving ¼ cup of the batter to put on top of the cream cheese filling.
In a medium mixing bowl, using a blender, mix together the softened cream cheese, sugar, vanilla and egg until well combined. Spread the cream cheese mixture in an even layer over the brownie batter. Use the remaining brownie batter and make small dollops on top of the cream cheese batter. Using a sharp knife or toothpick, swirl the cream cheese together with the dollops of brownie batter.
Bake the brownies for 30 minutes. Remove them from the oven and let them cool completely. Once they have cooled, lift the parchment paper out of the pan, then slice the brownies and serve!