Make the Brownie Batter:

1. Preheat the Oven: Preheat your oven to 350°F (175°C) and line an 8×8-inch baking pan with parchment paper, leaving an overhang for easy removal. Lightly grease the paper.
2. Melt the Butter: In a large microwave-safe bowl, melt the butter and let it cool slightly.
3. Mix the Sugars and Eggs: Add the granulated sugar and brown sugar to the melted butter and whisk until smooth. Beat in the eggs, one at a time, until fully incorporated. Stir in the vanilla extract and red food coloring until evenly mixed.
4. Incorporate Dry Ingredients: Sift the cocoa powder, flour, and salt into the wet ingredients. Gently fold the dry ingredients into the wet mixture until just combined, being careful not to overmix.

Optional Cream Cheese Swirl:

5. Prepare the Cream Cheese Mixture: In a small bowl, beat the softened cream cheese, sugar, egg yolk, and vanilla extract until smooth and creamy.

Assemble the Brownies:

6. Layer the Batter: Pour the brownie batter into the prepared baking pan and spread it evenly. Drop dollops of the cream cheese mixture over the brownie batter. Use a knife or skewer to swirl the cream cheese into the batter, creating a marbled effect.

Bake the Brownies:

7. Bake: Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
8. Cool: Allow the brownies to cool completely in the pan before lifting them out using the parchment overhang. Slice into squares and serve.