Prepare the Crust:
Preheat your oven to 325°F (163°C).
In a mixing bowl, combine graham cracker crumbs, sugar, and melted butter until everything is well incorporated.
Press the mixture firmly into the bottom of a springform pan, then bake for 10 minutes. Allow it to cool.
Make the Cheesecake Filling:
In a large mixing bowl, beat the softened cream cheese and sugar together until smooth and creamy.
Add in the vanilla extract and then incorporate the eggs one at a time, followed by the sour cream and heavy cream.
Gently fold in the blackberry purée until you achieve a swirled effect.
Bake the Cheesecake:
Pour the filling over the cooled crust. Bake in a water bath at 325°F (163°C) for about 50-60 minutes, or until the center is slightly jiggly.
Once it's done, turn off the oven and let the cheesecake cool inside with the door slightly ajar for an hour.
Prepare the Blackberry Topping:
In a small saucepan, combine fresh blackberries, sugar, and lemon juice over medium heat.
Add the cornstarch mixture and stir until the sauce thickens. Let it cool completely.
Assemble & Serve:
Once cooled, spread the blackberry topping over the cheesecake and refrigerate for at least 4 hours.
Garnish with fresh blackberries just before serving. Enjoy!