**Preheat and Prepare the Pan:** Preheat your oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper, leaving an overhang for easy removal.

**Make the Brownie Batter:** In a mixing bowl, whisk together melted butter and sugar until smooth. Add eggs, vanilla extract, and red food coloring, mixing until fully combined. Sift in the cocoa powder, flour, and salt, then gently fold the dry ingredients into the wet mixture until just combined.

**Prepare the Cream Cheese Swirl:** In a separate bowl, beat together cream cheese, sugar, egg yolk, and vanilla extract until smooth and creamy.

**Assemble:** Pour the brownie batter into the prepared pan, spreading it evenly. Drop spoonfuls of the cream cheese mixture on top and use a knife or skewer to swirl it into the batter for a marbled effect.

**Bake:** Bake for 30–35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Avoid overbaking for the best fudgy texture.

**Cool and Serve:** Let the brownies cool completely in the pan before lifting them out using the parchment paper. Cut into squares and enjoy.