Preheat your oven to 350°F (175°C). Grease an 8-inch square metal baking pan, then line it with parchment paper, leaving an overhang on two sides to facilitate easy removal. Lightly butter the parchment paper.

In a heatproof bowl, melt the butter and chopped dark chocolate together using short intervals in the microwave or over a double boiler. Stir until smooth and well combined. Set aside to cool slightly.

In a large mixing bowl, whisk together the sugar, eggs, vanilla extract, and red food coloring until the mixture is smooth and slightly thickened. Add the cooled chocolate mixture and whisk until fully incorporated. Gently stir in the flour and salt until just combined, ensuring no dry streaks remain. Do not overmix.

Pour the brownie batter into the prepared baking pan and spread it evenly into the corners with a spatula.

In a separate bowl, beat the cream cheese, sugar, egg, and vanilla extract together until completely smooth and creamy.

Spoon the cheesecake mixture in dollops over the brownie batter (approximately 8 spoonfuls). Using a knife or skewer, gently swirl the cheesecake into the brownie base, creating a marbled pattern.

Bake in the preheated oven for 35 to 40 minutes, or until the edges are lightly golden and a knife inserted into the cheesecake portion comes out clean.

Allow the brownies to cool completely in the pan on a wire rack. Once cooled, lift them out using the parchment paper and slice into squares. Store refrigerated for best texture.