01 - Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving an overhang on two sides for easy removal later.
02 - In a large bowl, whisk together melted butter, granulated sugar, and brown sugar until well combined and smooth.
03 - Beat in eggs, red food coloring, vanilla extract, and vinegar. Whisk vigorously until the mixture is smooth and uniform in color.
04 - Sift flour, cocoa powder, and salt directly into the wet mixture. Fold gently with a spatula until just combined—be careful not to overmix.
05 - Reserve 1/4 cup of the brownie batter for the marble swirl. Spread the remaining batter evenly across the bottom of the prepared pan.
06 - In a medium bowl, beat cream cheese, sugar, egg yolk, and vanilla extract until completely smooth and creamy, about 2 minutes.
07 - Drop spoonfuls of the cheesecake mixture over the brownie batter. Add small dollops of the reserved brownie batter on top. Use a knife or skewer to gently swirl the two batters together, creating a marbled pattern.
08 - Bake for 32–36 minutes. The brownies are done when the center is just set and a toothpick inserted comes out with a few moist crumbs—avoid overbaking for fudgy texture.
09 - Cool completely in the pan on a wire rack, about 2 hours. Use the parchment overhang to lift the brownies out, then cut into 16 equal squares.