Preheat oven to 350°F (175°C). Line a square baking pan with parchment paper.
Mix melted butter and sugar until smooth. Add eggs and vanilla.
Whisk in cocoa powder, flour, salt, and food coloring. Stir until combined.
In a separate bowl, mix cream cheese, sugar, egg yolk, and vanilla until creamy.
Spread most of the red velvet batter into the pan. Add spoonfuls of the cheesecake mixture.
Drizzle remaining red velvet batter on top. Swirl with a knife.
Bake 28–35 minutes or until set. Cool completely before slicing.