Preheat the oven to 180°C (fan). Grease a 20x20cm non-stick baking tin.
Pour the melted butter into the Stand Mixer bowl. Add in the sugar, the vanilla extract, cocoa powder,food coloring and vinegar. Start the mixer on a gentle speed and mix to form a thick, smooth batter. Add in the eggs, one at a time, allowing to incorporate, in between each egg. Spoon in the flour until combined.
Spoon out 3 tbsp of brownie batter into a bowl and add the rest to the greased baking tin. The reserved batter will be used for marbling the surface of the brownie with the cheesecake.
Clean the Stand Mixer bowl and add in the cream cheese, egg yolk, vanilla extract and sugar. Beat well until fully combined.Using a teaspoon, dollop the cheesecake mix over the top of the brownie batter. Smooth over, to reach all corners and is evenly distriuted.Next, spoon the remaining brownie batter over the cheesecake top. Use a cocktail stick to swirl the mixture to create a marbled effect.
Add to the pre-heated oven and bake for 30 minutes. Allow to chill in the fridge for 1 hour before slicing. Eat the same day for a light, cake-like finish, or leave for 1 day for a gooey brownie base.