Preheat your oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, allowing some overhang for easy removal later.
In a medium saucepan over low heat, combine the diced unsalted butter and chopped bittersweet chocolate. Stir frequently until both are melted and smooth. Remove from heat and let it cool slightly.
In a large mixing bowl, whisk together the granulated sugar and eggs until well combined. Add the melted chocolate mixture to the sugar and eggs, mixing thoroughly. Stir in the red food coloring until you achieve your desired shade. Then add the vanilla extract, sifted cocoa powder, all-purpose flour, and kosher salt. Mix until just combined; be careful not to overmix.
In another bowl, beat the softened cream cheese until smooth. Add the granulated sugar, flour, and vanilla extract, mixing until creamy and well incorporated. Gently fold in the egg whites until just combined.
Pour half of the brownie batter into the prepared baking pan, smoothing it out with a spatula. Next, dollop the cheesecake mixture over the brownie layer, spreading it evenly. Finally, pour the remaining brownie batter over the cheesecake layer, using a spatula to smooth it out.
Using a knife or a toothpick, gently swirl the brownie batter and cheesecake layer together to create a marbled effect. Be careful not to overdo it; you want to maintain distinguishable layers.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Avoid overbaking to keep the brownies fudgy.
Once baked, remove the brownies from the oven and allow them to cool in the pan for about 10 minutes. Using the parchment paper overhang, lift the brownies out of the pan and let them cool completely on a wire rack before slicing into squares.
