Begin by preheating your oven to 350°F (175°C). This ensures that your brownies bake evenly.
Line your 9x13 inch baking pan with parchment paper, leaving some overhang on the sides for easy removal later.
In a medium saucepan over low heat, combine the diced unsalted butter and coarsely chopped bittersweet chocolate. Stir gently until melted and smooth. Remove from heat and allow to cool slightly.
In a large mixing bowl, whisk together the granulated sugar and eggs until well combined. Add the melted chocolate mixture, red food coloring, and vanilla extract. Mix until smooth.
Sift the unsweetened cocoa powder, all-purpose flour, and kosher salt into the wet ingredients. Stir until just combined; a few flour streaks are okay.
In another bowl, beat the softened cream cheese until smooth. Gradually add the granulated sugar, 2 tablespoons of flour, and 1 teaspoon of vanilla extract. Mix until creamy and well combined. Fold in the two egg whites gently.
Pour half of the brownie batter into the prepared pan, spreading it evenly. Spoon dollops of the cheesecake mixture over the brownie layer. Finally, pour the remaining brownie batter over the cheesecake layer, swirling it gently for a marbled effect.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Allow the brownies to cool completely in the pan on a wire rack. Once cooled, lift the brownies out using the parchment overhang and slice into squares.
