Preheat and Prepare
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 large mixing bowl, whisk together melted butter and sugar until smooth. Add eggs, vanilla extract, and red food coloring, mixing until well combined.
Sift in cocoa powder, flour, and salt. Gently fold the dry ingredients into the wet ingredients until just combined.
Prepare the Cream Cheese Swirl (Optional)
In a separate bowl, beat cream cheese, sugar, egg yolk, and vanilla extract until smooth and creamy.
Assemble
Pour the brownie batter into the prepared pan and spread evenly. If using the cream cheese swirl, dollop spoonfuls on top of the batter and use a knife to create swirls.
Bake
Bake in the preheated oven for 25–30 minutes or until a toothpick inserted into the center comes out with a few moist crumbs. Avoid overbaking for fudgy brownies.
Cool and Serve
Let the brownies cool completely in the pan before lifting them out using the parchment paper. Slice into squares and serve.