Preheat the oven to 350°F (175°C) and prepare a 9x9-inch baking pan by greasing it with cooking spray or lining it with parchment paper for easy removal.

Melt the unsalted butter and semisweet chocolate together in a medium saucepan over low heat, stirring until smooth. Once melted, stir in both granulated and light brown sugar until well combined.

Add the large eggs and pure vanilla extract to the chocolate mixture, mixing until the batter is smooth. Then, blend in the red food coloring until you achieve a vibrant hue.

Sift together the all-purpose flour, unsweetened cocoa powder, and kosher salt in a separate bowl. Fold this dry mixture into the wet batter gently until just combined, taking care not to overmix.

Mix the cream cheese with the granulated sugar in another bowl until creamy and smooth. Set this mixture aside while you prepare to assemble the brownies.

Pour half of the brownie batter into the prepared pan, spreading it evenly. Next, spread the cream cheese mixture over the brownie base, followed by layering the remaining brownie batter on top.

Swirl a knife through the layers to create a beautiful marbled effect, then bake in the preheated oven for 30-35 minutes, or until a toothpick inserted in the center comes out mostly clean.

Cool the brownies in the pan; once cooled, cut them into squares for serving. Enjoy the rich, fudgy texture with the luscious cheesecake layer!