01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, allowing overhang for easy removal.
02 - Whisk melted butter, granulated sugar, and brown sugar until combined. Add eggs, vanilla, vinegar, and red food coloring. Whisk until smooth.
03 - Sift flour, cocoa powder, and salt into the wet mixture. Fold gently until just combined; avoid overmixing.
04 - Reserve 1/4 cup of batter. Spread remaining batter evenly in prepared pan.
05 - Beat cream cheese, sugar, egg yolk, and vanilla until smooth and creamy.
06 - Drop cheesecake mixture over brownie batter. Add spoonfuls of reserved red velvet batter. Gently swirl with skewer or knife for marbled effect.
07 - Bake for 33–36 minutes until center is just set and toothpick inserted at edge shows moist crumbs.
08 - Cool completely in pan, then lift out and cut into squares.