Creating the perfect Blackberry Cheesecake with Homemade Berry Sauce is a delightful process. Follow these steps to ensure success:

1. Preheat the Oven: Preheat your oven to 325°F (160°C). Grease a 9-inch springform pan.

2. Prepare the Crust: In a mixing bowl, combine graham cracker crumbs, melted butter, and sugar. Press the mixture firmly into the bottom of the prepared springform pan. Bake for 10 minutes, then remove and let cool.

3. Make the Cheesecake Filling: In a large mixing bowl, beat the softened cream cheese and sugar until smooth. Add the vanilla extract and mix well. Incorporate the eggs one at a time, mixing slowly after each addition. Finally, add the sour cream and blackberry puree, mixing until combined.

4. Bake the Cheesecake: Pour the cheesecake filling over the cooled crust. Bake in the preheated oven for 50-60 minutes or until the edges are set but the center still has a slight jiggle. Turn off the oven, crack the door, and let the cheesecake cool in the oven for 1 hour.

5. Chill the Cheesecake: After cooling, refrigerate the cheesecake for at least 4 hours or overnight for best results.

6. Prepare the Berry Sauce: In a saucepan over medium heat, combine the mixed berries, sugar, and lemon juice. Cook until the berries start to break down, about 5-7 minutes. If desired, mix cornstarch with a tablespoon of water and add to the sauce for thickening. Cook for an additional 2-3 minutes until thickened. Remove from heat and let cool.

7. Serve: Once the cheesecake is chilled, carefully remove it from the springform pan. Slice and serve each piece with a generous drizzle of homemade berry sauce.