01 - Preheat oven to 350°F. Line an 8 x 8 inch square baking pan with parchment paper, leaving an overhang on two sides for easy removal.
02 - In a medium bowl, whisk melted butter and granulated sugar until fully combined. Beat in eggs, vanilla extract, and red food coloring until smooth.
03 - Sift in all-purpose flour, cocoa powder, and salt. Gently fold mixture with a spatula until just incorporated. Spread about three-quarters of the red velvet batter evenly in the prepared pan. Reserve remaining batter.
04 - In a separate bowl, beat softened cream cheese and granulated sugar until creamy. Add egg and vanilla extract, mixing until smooth.
05 - Carefully pour cheesecake batter over the red velvet layer, spreading evenly to the edges. Drop reserved red velvet batter in small dollops over the top. Use a knife or skewer to gently swirl the batters for a marbled effect.
06 - Bake for 33 to 37 minutes, or until the center is just set and a toothpick inserted comes out mostly clean with a few moist crumbs.
07 - Allow to cool completely in the pan. Refrigerate for at least 1 hour. Lift out using parchment overhang and slice into squares before serving chilled.