Preheat your oven to 350°F and grease an 8-inch square baking pan thoroughly with butter or cooking spray, making sure to coat the bottom and all sides evenly. This prevents sticking and ensures clean edges when you cut the brownies later.

Melt the unsalted butter in a large mixing bowl over low heat or in the microwave in 30-second intervals, stirring between pulses until completely smooth. Add the 1 cup granulated sugar, 2 1/4 teaspoons vanilla extract, sifted cocoa powder, salt, red food coloring, and white vinegar, stirring until well combined and the color is evenly distributed throughout. In a separate small bowl, beat the 2 room temperature eggs together, then add them to the butter mixture along with the all-purpose flour, stirring just until combined—don't overmix, as this keeps the brownies fudgy. Reserve about 3-4 tablespoons of this batter in a small bowl and set aside; you'll use this later for the swirl.

While the oven preheats, beat the softened cream cheese in a clean bowl for about 30 seconds until smooth and creamy. Add the 1/4 cup granulated sugar, 1 egg yolk, and 3/4 teaspoon vanilla extract, beating for about 1 minute until the mixture is light and fully combined. I like to make sure my cream cheese is truly room temperature before mixing—cold cream cheese can be lumpy and won't swirl as beautifully.

Pour the majority of the red velvet brownie batter from Step 2 (everything except the reserved 3-4 tablespoons) into the prepared pan, spreading it evenly with a spatula. Dollop the cream cheese mixture from Step 3 over the brownie batter in spoonfuls, distributing it across the entire surface. Top with the reserved brownie batter by dropping small spoonfuls over the cream cheese layer. Using a knife, zigzag through the layers in one direction, then zigzag back in the opposite direction to create a decorative swirl pattern—don't overwork it, or you'll lose the distinct swirl effect.

Bake the brownies in the preheated 350°F oven for 28-30 minutes, until a toothpick inserted into the red velvet portion (not the cream cheese) comes out with just a few fudgy crumbs—it shouldn't be completely clean, as this indicates they're baked perfectly. The edges should look set and slightly pulled away from the pan. I find that slightly underbaking these brownies keeps them extra fudgy and prevents the cream cheese from drying out.

Remove the pan from the oven and let the brownies cool completely in the pan at room temperature—this usually takes 1-2 hours. Cooling them in the pan helps them set properly and makes them easier to cut into clean squares without the swirl layers sliding apart. Once fully cooled, cut into 9 or 16 squares depending on your preferred size.