01 - Preheat the oven to 350°F. Line an 8x8 inch baking pan with parchment paper, ensuring an overhang for easy removal.
02 - In a large bowl, whisk together melted butter and granulated sugar until well combined. Incorporate eggs, vanilla extract, and red food coloring; mix until the mixture is smooth and evenly colored.
03 - Sift in all-purpose flour, cocoa powder, and salt. Gently fold the dry ingredients into the wet mixture with a spatula until just combined. Avoid overmixing.
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, thoroughly beat softened cream cheese, granulated sugar, egg yolk, and vanilla extract until the mixture is completely smooth and free of lumps.
06 - Drop spoonfuls of the smooth cream cheese mixture over the brownie batter in the pan. Then, add small dollops of the reserved brownie batter on top of the cream cheese.
07 - Using a knife or a skewer, gently swirl the cream cheese and brownie batters together to create an attractive marbled effect.
08 - Bake in the preheated oven for 33 to 36 minutes, or until the center is just set and a toothpick inserted comes out with a few moist crumbs (not wet batter).
09 - Allow the brownies to cool completely in the pan on a wire rack before carefully lifting them out by the parchment paper overhang and cutting them into individual squares for serving.