Preheat oven to 300°F (150°C). Line a springform pan with parchment and wrap the bottom with foil.
Melt the chocolate in a heatproof bowl over simmering water. Set aside to cool slightly.
In a large bowl, beat cream cheese and sugar until smooth. Add sour cream, cocoa powder, and vanilla. Mix well.
Add eggs, one at a time, mixing until just combined. Stir in melted chocolate and a pinch of salt.
Pour the batter into the prepared pan and smooth the top.
Bake for 55-60 minutes, or until the edges are set and the center is slightly jiggly.
Turn off the oven, leave the door slightly ajar, and cool the cheesecake for 1 hour inside.
Chill in the fridge for at least 4 hours or overnight.
For the compote: In a saucepan, heat blackberries, sugar, and lemon juice over medium heat until berries release juice.
Stir in cornstarch slurry and cook until thickened. Let cool before serving with cheesecake.