Prep the pan and oven: Preheat the oven to 350°F (175°C). Line an 8-inch square baking pan with parchment, leaving overhang for easy lifting. Lightly grease the parchment.

Make the cheesecake mixture: In a bowl, beat the cream cheese, sugar, egg yolk, vanilla, and a pinch of salt until smooth and creamy. Set aside.

Whisk the wet ingredients: In a separate bowl, whisk the melted butter, granulated sugar, and brown sugar until glossy. Add the eggs and vanilla and whisk until well combined.

Add color and cocoa: Stir in the red food coloring and cocoa powder until evenly tinted. Adjust color as needed to achieve a deep red.

Finish the dry ingredients: In a small bowl, mix flour, baking powder, and salt. Sift if lumpy. Add to the red batter and fold gently until just combined. Stir in the vinegar at the end. Do not overmix.

Assemble layers: Pour about 2/3 of the red batter into the prepared pan and spread evenly. Dollop the cheesecake mixture over the top in large spoonfuls. Spoon the remaining red batter in between the cheesecake dollops.

Create the swirl: Use a butter knife or skewer to gently swirl the mixtures together. Aim for figure-eight motions and avoid over-swirling to keep distinct ribbons.

Bake: Bake for 28–35 minutes, until the edges are set and a toothpick inserted 2 inches from the edge comes out with a few moist crumbs. The center should have a slight jiggle from the cheesecake but not be soupy.

Cool and set: Let the pan cool on a rack for 1 hour. For clean slices and best texture, chill for at least another 1–2 hours before cutting.

Slice and serve: Lift out using the parchment and cut into squares with a sharp knife, wiping the blade between cuts for neat edges.