First, make the blackberry sauce: add the blackberries and sugar to a small saucepan. Crush lightly with a wooden spoon, and turn the heat to medium. Let the blackberries cook until soft and falling apart (about 10 minutes). Push the blackberries through a sieve to collect all of the juice and discard the seeds. Set aside.
Next, make the brownies: combine the butter, sugar and cocoa powder in a medium microwave-safe bowl. Heat on HIGH for 30 seconds.
Stop, stir the mixture, and then place it back in the microwave for another 30 seconds.
Stir the brownie mixture gently to cool for about 3-4 minutes, and then stir in the salt and vanilla to further cool it.
Once the brownie mixture feels warm (but not hot) to the touch, add the egg and stir until combined.
Finally, add the flour, and beat for at least 50 strokes (the more you stir brownie batter, the chewier the brownies will be!)
Preheat the oven to 325-F.
Line a 9x5x3” loaf pan with parchment paper, leaving extra on the ends to serve as handles.
Spread the brownie mixture evenly in the bottom of the pan.
Next, make the cheesecake filling: combine all ingredients and beat until smooth with an electric mixer, about 3 minutes.
Pour the cheesecake mixture over the brownies, and gently smooth.
Next, drizzle the blackberry sauce on top of the cheesecake, and use a toothpick to gently swirl it into the cheesecake layer (try not to swirl it into the brownie layer).
Bake for 45 minutes, or until the edges of the cheesecake start to turn golden brown, and a toothpick inserted to the cheesecake comes out mostly clean.
Let the brownies cool in the pan to room temperature, and then slice. Refrigerate for the easiest slicing! Enjoy!