1. Preheat the oven to 350°F (175°C). Line an 8×8-inch baking pan with parchment paper and lightly grease it.

2. In a medium bowl, beat the softened cream cheese, sugar, egg yolk, and vanilla extract until smooth and creamy. Set aside.

3. In a large mixing bowl, whisk together melted butter and sugar until glossy.

4. Add the eggs one at a time, mixing well after each addition.

5. Stir in vanilla extract, red food coloring, and vinegar until fully combined.

6. In a separate bowl, whisk together cocoa powder, flour, and salt.

7. Fold the dry ingredients into the wet ingredients until no dry streaks remain.

8. Spread about three-quarters of the brownie batter into the prepared baking pan.

9. Spoon the cheesecake filling evenly over the brownie batter.

10. Add dollops of the remaining brownie batter over the cheesecake layer.

11. Use a knife or skewer to gently swirl the layers together to create a marbled effect.

12. Bake for 32 to 38 minutes or until the edges are set and the center still looks slightly soft.

13. Remove from the oven and cool completely at room temperature.

14. Refrigerate for at least 1 hour before slicing for the cleanest cuts.

15. Slice into squares and serve chilled or slightly warm.