Heat the oven to 350°F (177°C). Line an 8 x 8-inch square pan with parchment paper, leaving enough overhang on two sides to lift out the cooled brownies.

Whisk the melted butter and granulated sugar together in a medium bowl. Add the egg, vanilla extract, red food coloring, and white vinegar, then whisk until the mixture looks smooth and evenly colored.

In a separate bowl, stir together the flour, natural cocoa powder, and salt. Fold the dry mixture into the butter mixture just until no dry streaks remain, taking care not to overmix.

Set aside approximately 2 to 3 tablespoons of the brownie batter for the swirl. Spread the remaining batter evenly in the parchment-lined pan.

Beat the softened cream cheese, sugar, egg yolk, and vanilla until smooth. Spread this cheesecake mixture gently over the brownie batter.

Spoon the reserved brownie batter over the cheesecake layer in small dots or thin lines. Drag a knife or skewer through the top to create a marbled pattern without disturbing the bottom layer.

Bake for 28 to 32 minutes, until the cheesecake is set around the edges and the center still has a slight wobble. A toothpick inserted into the brownie portion should come out with moist crumbs rather than wet batter.

Cool the brownies completely in the pan for at least 1 hour. For firmer layers and cleaner cuts, refrigerate them for 1 to 2 hours before lifting them out and slicing into 16 squares.