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 and sugar until smooth. Add eggs, vanilla extract, and red food coloring; whisk until fully combined.
03 - Sift in the flour, cocoa powder, and salt. Fold gently with a spatula until just combined—do not overmix.
04 - Reserve about ¼ cup of the brownie batter for swirling. Spread the remaining batter evenly into the prepared pan.
05 - In a medium bowl, beat the cream cheese until smooth. Add sugar, egg yolk, and vanilla; beat until creamy and well blended.
06 - Drop spoonfuls of the cheesecake mixture over the brownie batter in the pan. Dollop the reserved brownie batter on top.
07 - Use a knife or skewer to gently swirl the cheesecake and brownie layers together to create a marbled effect.
08 - Bake for 32–35 minutes, or until the center is just set and a toothpick inserted comes out with a few moist crumbs.
09 - Cool completely in the pan on a wire rack. Lift out using the parchment overhang, slice into squares, and serve.