Preheat your oven to 350°F (175°C) and prepare an 8x8 inch baking pan by lining it with parchment paper or greasing it slightly for easy removal later.

Whisk together the melted butter, sugar, cocoa powder, red food coloring, vanilla extract, and vinegar in a medium bowl until fully combined, creating a silky mixture.

Add eggs one at a time to the butter mixture, whisking in between each addition until smooth. Gently incorporate the flour and salt until just combined; reserve 1/4 cup of this batter for later!

Spread the majority of the brownie batter evenly into the prepared pan, ensuring an even base for the delicious cheesecake layer on top.

Beat the cream cheese, sugar, egg yolk, and a touch of vanilla extract in another bowl until smooth and creamy. Pour this cheesecake mixture over the brownie layer.

Dollop the reserved brownie batter in small spoonfuls on top of the cheesecake mixture, and with a toothpick or knife, gently swirl to create a marbled effect.

Bake for 30-35 minutes, or until the edges are set and the center remains slightly jiggly. Allow them to cool completely in the pan before slicing.

For an extra special touch, top with a dusting of powdered sugar or a drizzle of chocolate sauce.