Preheat the oven to 180°C (160°C fan). Line a 20cm square baking tin with parchment paper, leaving two sides overhanging like handles. The paper should sit flush against the corners — press it in with your fingertips until you hear it crinkle flat.

Melt the butter in a large mixing bowl. Microwave in 30-second bursts, stirring each time, until it's completely liquid and smells nutty and warm. Whisk in both sugars until the mixture looks like wet sand — gritty, glossy, and darker than when you started.

Add the eggs and vanilla. Whisk vigorously for a full minute. The batter should thicken noticeably, becoming paler and pulling away from the sides of the bowl in ribbons when you lift the whisk. This aeration is what gives the brownie its crackly top.

Sift the flour, cocoa, and salt directly over the batter. Fold gently with a spatula, scraping the bottom of the bowl. Stop when you can no longer see any white flour streaks — about twelve folds. The batter should be thick, fudgy, and smell deeply of chocolate.

Spoon the brownie batter into the prepared tin. Use the spatula to spread it evenly into the corners. It will be quite stiff — that is exactly right.

Make the cheesecake layer in the same bowl. Add the softened cream cheese, 50g sugar, egg yolk, and ½ teaspoon vanilla. Mash with a fork until smooth, then switch to a spoon and beat for thirty seconds until it looks like thick yogurt — pale, silky, and completely lump-free.

Spoon dollops of cheesecake mixture over the brownie batter. Aim for nine even blobs — three rows of three. Take a butter knife and drag it through both layers in an S-shape, working from left to right. Do this exactly five times; over-swirling muddies the pattern.

Bake for 26-30 minutes. At 26 minutes, the edges should look set and slightly pulling away from the paper, the centre should wobble just a little when you gently shake the tin, and the top should have a delicate, paper-thin crust. A skewer inserted two inches from the edge should come out with a few moist crumbs — not wet batter.

Cool in the tin on a wire rack for twenty minutes. The brownie will continue to cook from residual heat. After twenty minutes, lift it out using the parchment handles and transfer to the rack to cool completely. The top should feel firm and matte, not sticky.

Chill for at least one hour before slicing. I know it's hard to wait, but a chilled brownie cuts cleanly. Use a long, sharp knife and wipe it between each cut. You should see distinct, creamy swirls against the dark, fudgy brownie.