01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, allowing overhang for easy removal.
02 - Whisk melted butter and sugar in a large bowl until smooth. Add eggs, vanilla extract, and red food coloring; whisk until fully incorporated.
03 - Sift flour, cocoa powder, and salt into the wet mixture. Fold gently with a spatula until just combined—avoid overmixing to maintain fudgy texture.
04 - Reserve ¼ cup of batter for swirling. Spread remaining batter evenly across the prepared pan.
05 - Beat cream cheese until smooth. Blend in sugar, egg yolk, and vanilla extract until creamy and uniform.
06 - Drop spoonfuls of cheesecake mixture over brownie batter. Dollop reserved brownie batter on top. Use a knife or skewer to swirl layers together gently for marbled effect.
07 - Bake for 32–35 minutes until center is just set and toothpick inserted comes out with moist crumbs.
08 - Cool completely in pan on wire rack. Lift using parchment overhang and cut into squares before serving.