Preheat your oven to 350°F (175°C) and prepare an 8x8-inch baking pan by greasing and lining it with parchment paper.

In a large mixing bowl, whisk together the melted unsalted butter and granulated sugar until well combined. Add eggs, stirring after each addition, then mix in red food coloring, vanilla extract, and salt.

Sift together all-purpose flour and cocoa powder in a separate bowl. Gradually fold this into the brownie base until just blended.

Beat the cream cheese with an electric mixer until smooth. Add the additional egg and sugar, mixing until incorporated.

Pour half of the brownie batter into the pan and dollop half of the cheesecake mixture on top. Swirl with a knife or toothpick.

Repeat layering with remaining brownie and cheesecake mixtures, swirling again to create a marbled effect.

Bake for 35-40 minutes, until a toothpick comes out with a few moist crumbs. Avoid overbaking.

Let the brownies cool completely in the pan on a wire rack before slicing and serving.