Preheat oven to 200C/180C Fan/Gas 6. Line an 8″ square baking tin with greaseproof paper.
In a small bowl, break up the dark chocolate and melt in the microwave in 20 second intervals, stirring in between to make sure it doesn't burn. Alternatively, set up a double boiler. Do this by placing a heatproof bowl over a small pot of simmering water. Add the chocolate to the heatproof bowl and stir until melted. Set aside.
In a large bowl or the bowl of a stand mixer combine the melted butter, and both the brown and granulated sugars on a medium speed until totally combined.
Add the eggs and vanilla and mix again. Then check that the chocolate has cooled a little before adding in and combining.
Add in the flour and cocoa powder, and fold together. Reserve about 1/4 cup of the batter, pouring the rest into the prepared tin.
Make the cheesecake layer by combining all ingredients in a small bowl and mixing with a spoon. Make sure the chocolate has cooled a little before adding it!
Pour this cheesecake mixture over the brownie layer. Then, mix together that reserved brownie batter with a little water to thin it out (about 50ml) and drizzle over the cheesecake. Swirl to make a nice pattern!
Bake for 35-40 minutes. It will look puffy and should not wobble much at all. Let cool on a wire rack. Once completely cooled, slice and serve!