01 - Preheat the oven to 350°F (175°C). Line an 8x8 inch baking pan with parchment paper, allowing an overhang on all sides for easy removal.
02 - In a large mixing bowl, whisk together the melted unsalted butter and 1 cup granulated sugar until well combined. Incorporate the large eggs, 1 teaspoon vanilla extract, and red food coloring, mixing until the batter is smooth.
03 - Sift the all-purpose flour, unsweetened cocoa powder, and 1/4 teaspoon salt into the wet mixture. Gently fold with a spatula until just combined, taking care not to overmix the batter.
04 - Reserve 1/4 cup of the prepared brownie batter for the swirl. Evenly spread the remaining brownie batter into the parchment-lined baking pan.
05 - In a separate bowl, beat the softened cream cheese, 1/4 cup granulated sugar, egg yolk, and 1/2 teaspoon vanilla extract until the mixture is completely smooth and free of lumps.
06 - Drop spoonfuls of the cream cheese mixture over the brownie batter in the pan. Distribute dollops of the reserved brownie batter on top of the cream cheese layer.
07 - Using a knife or a skewer, gently swirl the cream cheese and brownie batters together to create an attractive marbled effect across the surface.
08 - Bake for 33–36 minutes, or until the center is just set and a toothpick inserted into the brownie comes out with a few moist crumbs, not wet batter.
09 - Allow the brownies to cool completely within the pan before carefully lifting them out using the parchment paper overhang. Once cooled, cut into squares for serving.