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

In a mixing bowl, whisk together melted butter and sugar until combined. Add eggs, vanilla extract, and red food coloring, mixing well.

Gradually sift in cocoa powder, flour, and salt, folding until just combined to avoid overmixing.

In a separate bowl, beat softened cream cheese and sugar until smooth, then add additional egg and vanilla extract, mixing until blended.

Pour three-quarters of brownie batter into the pan, dollop cheesecake mixture on top, and swirl remaining brownie batter to create a marbled effect.

Bake for 30-35 minutes until edges are set and a toothpick comes out mostly clean.

Let cool in the pan for 10 minutes, then lift out using parchment paper and cool completely for 30 minutes before slicing.

Slice into squares and serve with whipped cream or a drizzle of chocolate sauce.