Preheat your oven to 350°F (175°C) and line an 8x8-inch baking pan with parchment paper.

In a large mixing bowl, whisk together melted butter and sugar until smooth. Incorporate eggs, vanilla extract, and red food coloring, blending until fully combined.

Sift in cocoa powder, flour, and salt, folding gently to maintain fudgy texture.

In a separate bowl, beat softened cream cheese with additional sugar until creamy. Add the additional egg and mix until lump-free.

Spread 3/4 of the brownie batter evenly in the prepared pan. Pour the cheesecake layer over it, smoothing it out.

Dollop remaining brownie batter on top, swirling gently with a knife to create a marbled effect.

Bake for 30-35 minutes until edges are set and center is slightly moist. A toothpick should come out with a few moist crumbs.

Allow brownies to cool completely in the pan, then chill in the refrigerator for at least 30 minutes before slicing.

Lift out of the pan, cut into squares, and serve plain or with whipped cream or chocolate sauce.