Preheat your oven to 325°F (160°C).

To make the crust, combine graham cracker crumbs, sugar, and melted butter in a mixing bowl. Stir until well combined. Press the mixture firmly into the bottom of the springform pan. Bake in the preheated oven for 10 minutes. Remove and let cool.

For the cheesecake filling, beat the cream cheese and sugar together in a mixing bowl until smooth. Add the vanilla extract and mix well.

Add the eggs one at a time, mixing on low speed after each addition until just combined. Do not overmix. Then add sour cream and flour, and beat until incorporated.

Pour the cheesecake filling over the cooled crust. Bake for 50-60 minutes, until the edges are set but the center is slightly jiggly. Turn off the oven and let the cheesecake cool in the oven with the door ajar for about 1 hour.

While the cheesecake cools, prepare the blackberry topping. In a saucepan, combine blackberries, sugar, cornstarch, lemon juice, and water. Bring to a simmer over medium heat, stirring gently to avoid smashing the blackberries. Cook for about 5-7 minutes until the mixture thickens. Remove from heat and let cool slightly.

Once the cheesecake has cooled, pour the blackberry topping over the surface, spreading it evenly.

Refrigerate the cheesecake for at least 4 hours, or preferably overnight, before removing from the springform pan and serving.