01 - Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, allowing overhang on opposite sides for easy removal later.
02 - In a large bowl, whisk together melted butter, granulated sugar, and brown sugar until fully combined and smooth.
03 - Beat in eggs, red food coloring, vanilla extract, and vinegar. Whisk vigorously until the mixture is uniformly smooth and slightly thickened.
04 - Sift flour, cocoa powder, and salt directly into the wet mixture. Using a spatula, fold gently until just combined—be careful not to overmix, which can make brownies tough.
05 - Reserve 1/4 cup of the brownie batter in a small bowl for the swirl topping. Spread the remaining batter evenly across the bottom of the prepared pan.
06 - In a medium bowl, beat cream cheese and granulated sugar until smooth and creamy. Add egg yolk and vanilla, continuing to beat until completely incorporated and lump-free.
07 - Drop spoonfuls of cheesecake mixture randomly over the brownie batter. Add small dollops of the reserved brownie batter on top. Use a knife or skewer to gently swirl through both layers, creating a marbled pattern without over-mixing.
08 - Bake for 32 to 36 minutes. The brownies are done when the edges are set but the center still has a slight jiggle, and a toothpick inserted in the center comes out with a few moist crumbs.
09 - Let the brownies cool completely in the pan on a wire rack—this is crucial for clean cuts. Once cool, use the parchment overhang to lift the entire slab out, then cut into 16 equal squares.