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 combined.
03 - Sift flour, cocoa powder, and salt into the wet mixture. Fold gently with a spatula until just combined, being careful not to overmix.
04 - Reserve ¼ cup of brownie batter for swirling. Spread remaining batter evenly in the prepared pan.
05 - Beat cream cheese until smooth. Add sugar, egg yolk, and vanilla; beat until creamy and well blended.
06 - Drop spoonfuls of cheesecake mixture over brownie batter. Dollop reserved brownie batter on top. Gently swirl layers together with a knife or skewer.
07 - Bake 32-35 minutes until center is just set and a toothpick inserted comes out with a few moist crumbs.
08 - Cool completely in the pan on a wire rack. Lift using parchment overhang, slice into squares, and serve.