01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, allowing overhang for easy removal later.
02 - Whisk melted butter and granulated sugar in a large bowl until smooth. Add eggs, vanilla extract, and red food coloring; whisk until fully combined.
03 - Sift flour, cocoa powder, and salt into the wet mixture. Fold gently with a spatula until just incorporated, taking care not to overmix.
04 - Reserve ¼ cup of brownie batter for swirling. Spread remaining batter evenly across the prepared pan.
05 - Beat softened cream cheese until smooth. Add sugar, egg yolk, and vanilla extract; continue beating until creamy and well blended.
06 - Drop cheesecake mixture spoonfuls over brownie batter. Dollop reserved brownie batter on top, then use a knife or skewer to gently swirl layers together for marbled effect.
07 - Bake for 32-35 minutes until center is just set and a toothpick inserted comes out with moist crumbs. Avoid overbaking for fudgy texture.
08 - Cool completely in pan on wire rack. Lift out using parchment overhang, slice into 16 squares, and serve.