Preheat oven to 350. Spray an 8x8 baking dish with nonstick cooking spray and set aside.
In a large bowl, combine melted butter sugar, vanilla, cocoa powder, salt, food coloring, and vinegar, mixing after each addition. Whisk the eggs into the cocoa mix. Mix in the flour until lightly combined. Pour the batter into the prepared baking pan, saving ⅓ to ¼ cup of the batter for the cream cheese layer.
In the bowl of an electric mixer, cream together cream cheese, sugar, egg, and vanilla until smooth. Spread the cream cheese on top of the brownie batter in the pan. Put the remaining cocoa batter over the cream cheese layer. Using the tip of a knife, swirl through the cream cheese mixture to create a swirl pattern.
Bake the brownies for 30 minutes. Remove to a cooling rack and allow them to cool completely before cutting.