Preheat the Oven: Start by preheating your oven to 350°F (175°C). Line an 8×8-inch baking pan with parchment paper and lightly grease it to prevent sticking.
Make the Brownie Batter: In a large mixing bowl, melt 1/2 cup of unsalted butter. Once melted, whisk in 1 cup of granulated sugar and 1/4 cup packed brown sugar until smooth. Add 2 large eggs one at a time, mixing well after each addition. Stir in 1 tsp of vanilla extract and 1 tbsp red food coloring until fully combined. Finally, fold in 1/4 cup of unsweetened cocoa powder, 3/4 cup all-purpose flour, and 1/2 tsp of salt. Mix until just combined; be careful not to overmix!
(Optional) Prepare the Cream Cheese Mixture: In a separate bowl, beat together 4 oz of softened cream cheese, 1/4 cup of granulated sugar, 1 large egg yolk, and 1/2 tsp of vanilla extract until the mixture is smooth and creamy.
Assemble the Brownies: Pour the brownie batter into the prepared baking pan, spreading it evenly. Dot the batter with the cream cheese mixture and use a knife or toothpick to swirl it gently for a marbled effect.
Bake: Place the pan in the preheated oven and bake for 30-35 minutes. To check for doneness, insert a toothpick into the center—the toothpick should come out with moist crumbs, not wet batter. Once done, allow the brownies to cool completely in the pan. Use the parchment paper to lift them out, slice into squares, and enjoy!