01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, allowing overhang on sides for easy removal.
02 - Whisk melted butter with granulated and brown sugars in a large bowl until combined. Add eggs, red food coloring, vanilla extract, and vinegar; whisk until smooth.
03 - Sift flour, cocoa powder, and salt into the wet mixture. Fold gently until just combined, being careful not to overmix.
04 - Beat cream cheese, sugar, egg yolk, and vanilla extract in a medium bowl until smooth and creamy.
05 - Reserve 1/4 cup brownie batter. Spread remaining batter evenly in prepared pan. Dollop cheesecake mixture over batter, then add reserved brownie batter in small spoonfuls. Use knife or skewer to gently swirl together for marbled effect.
06 - Bake 32-36 minutes until center is just set and toothpick inserted comes out with a few moist crumbs.
07 - Cool completely in pan on wire rack. Lift out using parchment overhang, slice into 16 squares, and serve.