01 - Preheat 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. Add eggs, vanilla, vinegar, and red food coloring. Whisk until smooth.
03 - Sift in flour, cocoa powder, and salt. Fold gently until just combined; do not overmix.
04 - Reserve 1/4 cup of the red velvet batter. Pour the remaining batter into the prepared pan and smooth the top.
05 - In a separate bowl, beat cream cheese, sugar, egg yolk, and vanilla until smooth and creamy.
06 - Dollop the cheesecake mixture over the brownie batter in the pan. Drop spoonfuls of reserved red velvet batter on top.
07 - Use a skewer or knife to gently swirl the cheesecake and red velvet batters together for a marbled effect.
08 - Bake for 33-36 minutes, or until the center is just set and a toothpick inserted into the edge comes out with a few moist crumbs.
09 - Cool completely in the pan, then lift out and cut into squares.