Preheat the oven to 400°F (200°C) and line a 8-inch (20 cm) square brownie/baking tin with baking parchment.
Melt the dark chocolate in the microwave in 20-second intervals, stirring regularly to make sure it doesn’t burn. Set aside to cool while making the brownie batter.
In a large mixing bowl, with an electric handheld whisk, or in the bowl of a stand mixer fitted with the whisk attachment, whisk together the melted butter and both sugars for 3 to 5 minutes until totally combined. Add the eggs, one at a time, mixing after each addition. Check the melted chocolate has cooled a little, and then gradually add it and mix to combine. Add the flour, cocoa powder, chopped white chocolate and blackberries and fold together. Transfer the batter into the lined tin.
Make the cheesecake layer by combining all ingredients in a small bowl and mixing with a spoon. Pour this over the brownies. Roughly fold together with a teaspoon and scatter over the remaining blackberries.
Bake in the oven for 20 to 30 minutes, until the cheesecake layer looks a little golden. The cheesecake may look a little wobbly but that’s fine; it sets as it cools.
Remove from the oven and leave to cool in the tin on a wire rack before slicing and serving!
The brownies will keep for up to 4 days in an airtight container.