Preheat your oven to 350°F (175°C). Line your 9x13-inch baking pan with parchment paper, leaving some overhang for easy removal later.
In a medium saucepan over low heat, combine the diced unsalted butter and chopped bittersweet chocolate. Stir gently until both are melted and smooth. Remove from heat and let cool slightly.
In a large mixing bowl, whisk together the granulated sugar and eggs until well combined. Add in the red food coloring and vanilla extract, stirring until you achieve a beautiful, vibrant color. Slowly pour in the cooled chocolate mixture, mixing until smooth.
Sift the cocoa powder, all-purpose flour, and kosher salt into the chocolate mixture. Gently fold the dry ingredients into the wet until just combined. Be careful not to overmix.
In another bowl, beat the cream cheese with an electric mixer until smooth. Add the granulated sugar, flour, and vanilla extract, mixing until there are no lumps. Then, add the egg whites and mix until fully incorporated.
Pour half of the brownie batter into the prepared pan, spreading it evenly. Drop spoonfuls of the cheesecake mixture over the brownie layer, then use a knife or toothpick to create swirls. Pour the remaining brownie batter on top and swirl again to combine.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Be careful not to overbake; you want these brownies to remain fudgy!
Allow the brownies to cool completely in the pan on a wire rack. Once cooled, lift them out using the parchment paper and cut them into squares. Serve these beautiful Red Velvet Cheesecake Brownies to your friends and family, or keep them all for yourself!