Preheat and Prepare: Preheat your oven to 180°C (160°C fan/Gas Mark 4). Grease and line a 20cm (8-inch) square baking tin with baking parchment, leaving an overhang on two sides to make it easier to lift out later.

Melt the Chocolate and Butter: In a heatproof bowl set over a saucepan of barely simmering water (a bain-marie), melt the butter and dark chocolate together. Stir occasionally until smooth and glossy. You can also do this in the microwave in 30-second bursts. For a detailed guide on this process, BBC Good Food has an excellent tutorial. Set aside to cool slightly.

Make the Brownie Batter: In a large bowl, using an electric mixer or a whisk, beat the 3 eggs and 225g of caster sugar together for 3-4 minutes until pale, thick, and voluminous. This step incorporates air, which gives the brownies a lovely light crust. Stir in the vanilla extract.

Combine Wet and Dry Ingredients: Pour the slightly cooled chocolate mixture into the egg mixture and gently fold it in. Sift the plain flour, cocoa powder, and salt over the bowl and fold again until just combined. I used to struggle with dry brownies until I discovered this technique: be careful not to over-mix at this stage, as it can make the final result tough. Stop as soon as you no longer see streaks of flour.

Assemble the Brownie Base: Pour about two-thirds of the brownie batter into your prepared tin and spread it out evenly with a spatula. Keep the remaining third for later.

Create the Cheesecake Filling: In a separate bowl, beat the room-temperature cream cheese and 75g of caster sugar with an electric mixer until smooth and creamy. Add the egg and vanilla extract and beat again until just combined. Don't over-beat it.

Layer and Swirl: Gently spoon the cheesecake mixture over the brownie base and spread it carefully to the edges. Dollop the remaining brownie batter in small spoonfuls over the cheesecake layer. Use a skewer or the tip of a knife to gently swirl the brownie batter into the cheesecake, creating a marbled effect. Be careful not to mix them together completely.

Add Blackberries and Bake: Gently press the fresh blackberries into the top of the mixture. Bake in the preheated oven for 35-40 minutes. The edges should be set, but the centre should still have a slight wobble. A skewer inserted into the brownie part should come out with moist, fudgy crumbs attached, not wet batter.

Cool Completely: This is the hardest part! You must let the brownies cool completely in the tin, first on a wire rack and then for at least 2-3 hours (or preferably overnight) in the fridge. This allows the cheesecake layer to set fully, ensuring clean, neat slices. Once chilled, use the parchment paper overhang to lift the slab out of the tin and cut into 16 squares.