Prep your pan and oven: Heat the oven to 350°F (175°C). Line an 8-inch square pan with parchment, leaving overhang for easy lifting.
Lightly spray the parchment.
Make the cheesecake swirl: In a medium bowl, beat softened cream cheese with sugar until smooth. Add egg yolk, vanilla, and a pinch of salt. Mix until creamy and lump-free; set aside.
Start the red velvet batter: In a large bowl, whisk melted butter and sugar until glossy.
Whisk in eggs one at a time, then vanilla.
Add color and cocoa: Whisk in red food coloring and cocoa powder until evenly tinted. Stir in the salt.
Finish the batter: Fold in the flour gently until just combined—do not overmix. Stir in the vinegar last.
The batter should be thick and shiny.
Layer and swirl: Spread about 3/4 of the red velvet batter into the prepared pan. Dollop the cheesecake mixture over the top in large spoonfuls. Add the remaining red velvet batter in small mounds between the cheesecake dollops.
Create the marbled look: Use a butter knife or skewer to gently swirl the two mixtures together.
Aim for wide, sweeping motions; avoid over-swirling so you keep clear ribbons of red and white.
Bake: Bake for 28–34 minutes, or until the edges are set and the center wobbles slightly but a toothpick inserted into the red velvet portion comes out with a few moist crumbs (not wet batter). If the top browns too fast, tent loosely with foil for the last 5 minutes.
Cool completely: Let the pan cool on a rack for at least 1 hour, then chill for 30–60 minutes before slicing. This helps the cheesecake set and gives cleaner cuts.
Slice and serve: Use the parchment to lift the slab out.
Wipe your knife between cuts for neat squares. Serve slightly chilled or at room temperature.