Preheat the oven to 180° C. Place baking paper in a square pan about 20 cm wide.
In a medium bowl, sift the flour with the cocoa powder, salt and mix well with a spoon.
Place the butter with the two types of sugar in a large bowl and cream with a balloon whisk for 2-3 minutes until smooth and creamy.
Add the eggs one at a time, beating for 30 seconds after each addition. Add the vanilla extract with the red food coloring and vinegar and beat until blended.
Add the flour mixture and beat just until there are no lumps and the ingredients are integrated so as not to over beat.
Pour the mixture into the baking pan and spread it until it is uniform.
For the cheesecake part and baking:
Place the cream cheese with the sugar, egg and vanilla extract in a medium bowl and beat with a balloon whisk for 2 minutes until very smooth and creamy.
Add spoonfuls of the cream cheese mixture on top of the brownie mixture and then spread it all over the surface drawing swirls using a wooden toothpick or a dull knife.
Bake the brownies at 180° C for 30 minutes until a wooden toothpick comes out almost clean with just a few crumbs.
Remove the brownies from the oven and let them cool for at least 20 minutes before cutting them. Then, unmold them and cut them into 12 equal parts.
The brownies can be stored in a tightly sealed tupperware container for up to 3 days at room temperature or up to 6 days in the refrigerator.