Prep the pan. Heat oven to 350°F (175°C). Line an 8-inch square pan with parchment, leaving overhang for easy lifting.
Make the blackberry swirl. In a small saucepan, combine blackberries, sugar, lemon juice, and cornstarch.
Cook over medium heat, mashing the berries, until thick and jammy, 3–5 minutes. Cool slightly.
Crush the Oreos. Pulse 24 Oreos in a food processor to fine crumbs (or crush in a bag). Stir in melted butter until evenly moistened.
Press firmly into the pan to form an even crust. Bake 8 minutes, then set aside.
Mix the brownie batter. Melt butter and chocolate together in a heatproof bowl over gently simmering water (or microwave in 20–30 second bursts). Whisk in sugars, then eggs and vanilla until glossy.
Sift in flour, cocoa, and salt. Fold just until combined.
Make the cheesecake mixture. Beat cream cheese with sugar until smooth. Mix in egg yolk and vanilla until creamy and lump-free.
Assemble. Spread brownie batter over the warm Oreo crust.
Dollop spoonfuls of cheesecake mixture on top, then add small spoonfuls of blackberry sauce between them.
Swirl. Use a butter knife or skewer to gently swirl the cheesecake and blackberry into the brownie. Don’t overmix—aim for visible ribbons.
Top (optional). Sprinkle with chopped Oreos and a pinch of flaky sea salt for contrast.
Bake. Bake 28–34 minutes, until the edges are set and the center has a slight jiggle. A toothpick should come out with moist crumbs, not wet batter.
Cool completely. Let the pan cool on a rack, then chill 1–2 hours for clean slices.
Lift out with parchment and cut into 16 squares with a warm knife.