01 - Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving an overhang for easy removal.
02 - In a large bowl, whisk together melted butter, granulated sugar, and brown sugar until combined.
03 - Add eggs, red food coloring, vanilla extract, and vinegar. Whisk until smooth.
04 - Sift in flour, cocoa powder, and salt. Fold gently until just combined; do not overmix.
05 - Reserve 1/4 cup of the batter for swirling. Spread the remaining batter evenly in the prepared pan.
06 - In a medium bowl, beat cream cheese, sugar, egg yolk, and vanilla until smooth and creamy.
07 - Dollop spoonfuls of the cheesecake mixture over the brownie batter. Add reserved brownie batter in small dollops.
08 - Use a knife or skewer to gently swirl the cheesecake and brownie batters together for a marbled effect.
09 - Bake for 32-36 minutes, or until the center is just set and a toothpick inserted comes out with a few moist crumbs.
10 - Cool completely in the pan on a wire rack. Lift out using the parchment overhang, slice into squares, and serve.