01 - Preheat oven to 350°F (175°C). Line an 8 x 8 inch (20 x 20 cm) square baking pan with parchment paper, allowing for overhang to lift brownies after baking.
02 - In a medium mixing bowl, combine melted butter and granulated sugar, whisking until smooth. Incorporate eggs, vanilla extract, and red food coloring, mixing until homogenous.
03 - Sift all-purpose flour, unsweetened cocoa powder, and salt into the bowl. Gently fold with a spatula until just combined. Spread approximately three-fourths of the batter evenly in the prepared pan, reserving the remainder.
04 - In a separate bowl, beat softened cream cheese and granulated sugar with an electric mixer or whisk until creamy. Add egg and vanilla extract, mixing until the mixture is smooth.
05 - Pour cheesecake mixture over the red velvet layer in the pan, smoothing gently to cover completely.
06 - Dollop reserved red velvet batter onto the cheesecake layer. Use a knife or skewer to gently swirl for a marbled appearance.
07 - Bake for 33 to 37 minutes, or until the center is set and a toothpick inserted in the middle comes out with a few moist crumbs attached.
08 - Allow to cool completely in the pan. Refrigerate for at least 1 hour to set before slicing and serving.