1. Prepare the Crust:

   – Preheat your oven to 325°F (160°C).

   – Combine graham cracker or Oreo crumbs, melted butter, and sugar in a bowl. Mix until the crumbs are evenly coated.

   – Press the mixture firmly into the bottom of a 9-inch (23cm) springform pan. Use a glass to smooth it out.

   – Bake the crust for 8-10 minutes, then let it cool while preparing the filling.

2. Make the Cheesecake Filling:

   – Beat the softened cream cheese in a large bowl until smooth and lump-free.

   – Gradually add sugar, mixing well. Stir in eggs one at a time, followed by sour cream, vanilla extract, and lemon juice. Mix just until combined to avoid overmixing.

3. Prepare the Blackberry Sauce:

   – In a saucepan, combine blackberries, sugar, and lemon juice over medium heat.

   – Cook until the berries release their juices and the mixture thickens (about 10 minutes). Strain through a fine mesh sieve to remove seeds.

   – For a thicker sauce, add the cornstarch slurry and simmer for an additional minute.

4. Assemble the Cheesecake:

   – Pour the cream cheese filling over the cooled crust. Smooth the top with a spatula.

   – Drizzle the blackberry sauce over the filling. Use a skewer or knife to swirl the sauce into the filling for a marbled effect.

5. Bake the Cheesecake:

   – Place the springform pan in a large roasting pan. Fill the roasting pan with hot water until it reaches halfway up the sides of the springform pan.

   – Bake for 60-70 minutes, or until the edges are set and the center is slightly jiggly.

6. Cool and Chill:

   – Turn off the oven and leave the cheesecake inside with the door slightly open for 1 hour.

   – Refrigerate the cheesecake for at least 6 hours or overnight to set completely.

7. Serve and Enjoy:

   – Remove the cheesecake from the springform pan. Garnish with fresh blackberries, whipped cream, or a drizzle of leftover blackberry sauce.

   – Slice and serve chilled for the best flavor.