1. Preheat oven to 350°F (176°C). Line the bottom of a 9×9 inch square pan with parchment paper and grease the sides.
2. Melt the butter in a microwave safe bowl, then transfer to a mixing bowl.
3. Add the sugar and whisk to combine.
4. Add the vanilla extract, vinegar, eggs and red food color and whisk until incorporated.
5. In another bowl, combine the dry ingredients.
6. Slowly add dry ingredients to wet ingredients and mix until combined. Set aside.
7. In another mixing bowl, add the cream cheese and sugar and mix until well combined and smooth.
8. Add the egg white and vanilla extract and mix until well combined.
9. Add about three quarters of the brownie batter to the bottom of the pan and spread into an even layer.
10. Drop spoonfuls of the cheesecake batter on top of the brownie, then use a toothpick to swirl it into the brownie layer below.
11. Drop spoonfuls of the remaining brownie batter on top of the cheesecake and use a toothpick to swirl it into the cheesecake.
12. Bake the bars for 25-30 minutes, then remove from the oven and allow to cool in the fridge.
13. Cut into bars and serve. Store bars in the fridge in an airtight container.