Preheat the oven to 350ºF (175ºC)
Line a 9x13-inch baking pan with parchment paper, leaving some overhang on the sides for easy removal.
In a microwave-safe bowl or using a double boiler, melt the butter and bittersweet chocolate together. Stir until smooth and let it cool slightly.
In a large bowl, whisk together the melted chocolate mixture, granulated sugar, and brown sugar. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract. Gently fold in the flour and salt until just combined.
In a separate bowl, beat the softened cream cheese, sugar, egg, and vanilla extract until smooth and creamy.
Pour the brownie batter into the prepared baking pan, spreading it evenly. Drop spoonfuls of the cream cheese mixture over the brownie batter. Use a toothpick or skewer to swirl the cream cheese mixture into the brownie batter, creating a marbled effect.
Place the pan in the preheated oven and bake for 35-40 minutes or until a toothpick inserted into the center comes out mostly clean with a few moist crumbs.
Allow the brownies to cool completely in the pan on a wire rack before lifting them out using the parchment paper overhang. Cut into squares and enjoy!