Butter an 8×8 inch baking pan. Line the bottom with parchment paper and grease the paper with butter.
In a stand mixer bowl, put in the butter, sugar, cocoa powder, vanilla, food coloring and salt and combine.
Add the white vinegar and mix. Add eggs and mix. Pour in the flour and mix until just combined.
Reserve 1/4 cup of batter in a small bowl. Pour the mixture into the prepared pan.
In another bowl, using a handheld mixer, mix together the cream cheese, sugar, vanilla and egg yolk. Pour this batter on top of the brownies batter. Spread so it will cover the brownies batter.
Put dollops of the reserved brownies batter on top of the cream cheese. Using a knife or toothpick make swirls at the top of the batter.
Bake for 30 minutes. Cool completely before taking it out of the pan.