1. Prepare the crust

1. Preheat your oven to 325°F (160°C). Grease a 9-inch (23 cm) springform pan and line the bottom with parchment paper.
2. In a medium bowl, mix the chocolate cookie crumbs and melted butter until the mixture resembles wet sand.
3. Press the mixture evenly into the bottom of the prepared springform pan.
4. Bake the crust for 8–10 minutes. Remove from the oven and let it cool while you prepare the filling.

2. Make the blackberry sauce

1. In a small saucepan over medium heat, combine the blackberries, sugar, and lemon juice. Cook for 5–7 minutes, stirring occasionally, until the blackberries break down and release their juices.
2. Add the cornstarch mixture to the saucepan and stir continuously for another 1–2 minutes until the sauce thickens.
3. Strain the sauce through a fine mesh sieve to remove seeds (optional). Set aside to cool.

3. Make the cheesecake filling

1. In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy (about 2 minutes).
2. Gradually add the sugar and mix until well combined.
3. Add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract.
4. Gently fold in the melted dark chocolate and sour cream until the mixture is smooth and velvety.

4. Assemble the cheesecake

1. Pour the dark chocolate cheesecake filling over the cooled crust and smooth the top with a spatula.
2. Drizzle the cooled blackberry sauce in small dollops over the surface of the cheesecake. Use a toothpick or skewer to swirl the blackberry sauce into the filling, creating a marbled effect.
3. Wrap the bottom of the springform pan tightly in aluminum foil and place it in a large roasting pan. Fill the roasting pan with hot water to about halfway up the sides of the springform pan (water bath method).

5. Bake

1. Bake the cheesecake in the preheated oven for 50–60 minutes, or until the edges are set but the center still has a slight jiggle.
2. Turn off the oven, crack the door slightly, and allow the cheesecake to cool inside the oven for 1 hour.
3. Remove the cheesecake from the water bath and let it cool to room temperature. Cover and refrigerate for at least 4 hours, or overnight, to set completely.

6. Serve

1. Carefully remove the cheesecake from the springform pan.
2. Garnish with fresh blackberries, dark chocolate shavings, and whipped cream, if desired. Slice and serve chilled for an indulgent treat.