Preheat the oven to 160°C (325°F). Grease the bottom of a 9-inch springform pan and line with baking paper.

In a mixing bowl, combine graham cracker crumbs, melted butter, and sugar. Mix until well combined. Press the mixture into the bottom of the springform pan to create an even crust. Bake for 10 minutes, then remove from the oven and let cool.

In another bowl, beat the softened cream cheese and granulated sugar together with a hand mixer until smooth and creamy. Add the vanilla extract and mix well.

Add the eggs one at a time, mixing well after each addition. Finally, incorporate the sour cream until the filling is smooth.

Pour the cheesecake filling onto the cooled crust in the springform pan. Bake in the preheated oven for 45-50 minutes or until the center is set but slightly jiggly.

Turn off the oven and crack the door slightly, allowing the cheesecake to cool gradually for about an hour. Then, remove it from the oven and refrigerate for at least 4 hours or overnight.

For the blackberry compote, combine fresh blackberries, sugar, lemon juice, cornstarch, and water in a saucepan. Cook over medium heat, gently mashing the blackberries until the mixture thickens, approximately 8-10 minutes. Let the compote cool.

Once the cheesecake is chilled, spread the blackberry compote evenly over the top. Slice and serve.