01 - Preheat oven to 350°F (175°C). Line an 8 x 8 inch square baking pan with parchment paper, leaving some overhang for easier removal.
02 - In a medium bowl, whisk the melted butter with granulated sugar until fully blended. Add the eggs, vanilla extract, and red food coloring, whisking until smooth.
03 - Sift in the all-purpose flour, cocoa powder, and salt. Gently fold with a spatula until just combined, avoiding overmixing. Spread approximately three-quarters of the red velvet batter in the prepared pan, reserving the remainder.
04 - In a separate bowl, beat the softened cream cheese and sugar with an electric mixer or whisk until creamy. Blend in the egg and vanilla extract, mixing until the mixture is smooth and homogenous.
05 - Carefully pour the cheesecake batter onto the red velvet base in the pan and spread evenly. Dollop the reserved brownie batter over the cheesecake layer. With a knife or skewer, gently swirl to create a marbled design.
06 - Bake for 33 to 37 minutes, or until the center is set and a toothpick inserted into the center comes out with a few moist crumbs attached.
07 - Let the brownies cool completely in the pan, then transfer to the refrigerator and chill for at least 1 hour. Remove from the pan using the parchment overhang, slice, and serve chilled.