Preheat your oven to 325°F (160°C).

In a mixing bowl, combine the graham cracker crumbs, melted butter, and sugar. Mix until all ingredients are well combined and resemble wet sand.

Press the mixture firmly into the bottom of the springform pan to form the crust. Set aside.

In a large mixing bowl, beat the softened cream cheese and sugar using an electric mixer until smooth and creamy.

Add the vanilla extract and mix until combined.

Add the eggs one at a time, mixing just until incorporated after each addition. Avoid overmixing to prevent cracking.

Fold in the sour cream using a rubber spatula until fully combined.

Pour the cheesecake filling over the prepared crust in the springform pan.

Bake in the preheated oven for 60 minutes, or until the edges are set but the center is still slightly jiggly.

Once baked, turn off the oven and leave the door slightly ajar, allowing the cheesecake to cool gradually for 1 hour.

Remove the cheesecake from the oven and let it chill in the refrigerator for at least 4 hours, preferably overnight.

While the cheesecake chills, prepare the blackberry topping. In a small saucepan, combine the blackberries, sugar, lemon juice, cornstarch, and water.

Cook over medium heat, stirring gently until the mixture begins to bubble and thicken, about 5-7 minutes.

Remove from heat and let the topping cool. Once cooled, spread it evenly over the chilled cheesecake.

Carefully remove the sides of the springform pan and slice the cheesecake into servings.