Preheat the oven to 350°F (175°C). Line an 8 x 8-inch (20 x 20 cm) metal baking pan with parchment paper, leaving an overhang on two opposite sides to help lift out the brownies later. Lightly crease the parchment into the corners so it sits flat against the pan.

Pour the 1/2 cup (113 g) melted, slightly cooled butter into a medium mixing bowl. Add the 1 cup (200 g) granulated sugar and whisk for about 1 minute, until the mixture looks glossy and evenly combined. It may still appear slightly grainy, which is normal.

Add the 2 large eggs, one at a time, whisking until each is fully incorporated. Mix in the 1 teaspoon (5 ml) vanilla extract, 1 teaspoon (5 ml) white vinegar, and 1 teaspoon (5 ml) red gel food coloring. The batter should become smooth, glossy, and evenly red. If the color looks streaky, continue mixing gently until no streaks remain.

Add the 3/4 cup (90 g) all-purpose flour, 2 tablespoons (10 g) sifted natural cocoa powder, and 1/4 teaspoon (1.5 g) fine salt. Fold gently with a rubber spatula until no dry flour remains. The finished batter should be thick, smooth, and spreadable rather than runny. Avoid vigorous mixing once the flour is added, which can make the brownies tough.

In a separate small bowl, beat the 4 ounces (113 g) softened cream cheese with the 3 tablespoons (38 g) granulated sugar until smooth. Add the 1 large egg yolk and 1/2 teaspoon (2.5 ml) vanilla extract. Mix until creamy and free of visible lumps. The mixture should be thick enough to sit in soft dollops on the brownie batter. If the cream cheese is lumpy, continue mixing until smooth.

Transfer the red velvet brownie batter to the prepared pan, reserving about 1/4 cup of batter for the decorative swirl. Spread the remaining batter evenly into the corners using a rubber spatula. The layer should be relatively level so the brownies bake evenly.

Spoon the cream cheese mixture in small dollops over the brownie batter. Add small spoonfuls of the reserved red velvet batter between the cream cheese dollops. Use a butter knife or wooden skewer to make a few gentle figure-eight motions through the surface. Stop once distinct red and white ribbons appear. Too much swirling will blend the layers and reduce the marbled appearance.

Place the pan on the center oven rack and bake at 350°F (175°C) for 30–35 minutes. The brownies are ready when the edges look set, the cream cheese surface no longer looks wet, and the center has only a slight movement when the pan is gently nudged. Insert a toothpick into a brownie-only section near the center. It should come out with a few moist crumbs, not liquid batter. Avoid checking through a cream cheese swirl, which can give a misleading result. If the center still looks wet, bake for another 3–5 minutes and check again.

Remove the pan from the oven and place it on a wire rack. Allow the brownies to cool in the pan for 1 hour. Use the parchment overhang to lift them carefully onto the rack or a cutting board. Let them rest for another 10 minutes, or until completely cool and firm enough to slice. If they still feel warm or soft, allow additional cooling time.

Using a sharp knife, cut the cooled brownies into 16 equal squares, making four rows in each direction. Wipe the knife clean between cuts to keep the cream cheese swirl neat. Serve at room temperature or slightly chilled, depending on your preferred texture.