01 - Preheat oven to 350°F. Line an 8-inch square baking pan with parchment paper, allowing overhang for easy removal.
02 - Whisk melted butter and granulated sugar in a large bowl until combined. Add eggs, vanilla extract, and red food coloring, mixing until smooth.
03 - Sift cocoa powder, flour, and salt into the wet mixture. Fold gently until just incorporated, being careful not to overmix.
04 - Reserve 1/4 cup of batter for topping. Spread remaining brownie batter evenly into the prepared pan, smoothing the surface.
05 - Beat cream cheese until smooth and creamy. Blend in sugar, egg yolk, and vanilla extract until fully incorporated.
06 - Drop cheesecake mixture over brownie base. Add dollops of reserved red velvet batter. Gently swirl with a skewer or knife to marble.
07 - Bake for 33-36 minutes until center is just set and toothpick inserted comes out with moist crumbs. Cool completely before slicing.