Step 1: Prepare the Oven and Tin
Preheat your oven to 180°C (160°C Fan). Line a 9×9-inch square baking tin with parchment paper, ensuring it covers the sides for easy removal.

Step 2: Make the Red Velvet Brownie Batter
In a bowl, beat together the unsalted butter and caster sugar until smooth and well combined. Mix the vanilla extract and red food coloring together to form a paste, then add this to the butter and sugar mixture and beat until incorporated.

Add the eggs, one at a time, beating well after each addition. Sift the cocoa powder and plain flour into the mixture, and fold them in until just combined. Stir in the white wine vinegar and mix lightly, ensuring not to overmix.

Step 3: Make the Cheesecake Swirl
In a separate bowl, beat together the full-fat cream cheese, caster sugar, and vanilla extract until smooth. Add the egg yolk and mix again until fully combined, forming a smooth cheesecake mixture.

Step 4: Assemble the Brownies
Pour about 90% of the brownie mixture into the prepared tin, spreading it evenly. Dollop the cheesecake mixture over the brownie batter, then add the remaining brownie batter on top in dollops. Use a skewer or knife to swirl the brownie and cheesecake batters together to create a marbled effect.

Step 5: Bake the Brownies
Bake in the preheated oven for 28–35 minutes. The brownies are done when the edges are set, but the center is slightly jiggly. Let the brownies cool in the tin for 20–30 minutes before transferring them to a wire rack to cool completely.