Preheat your oven to 325°F (160°C).
In a mixing bowl, combine the graham cracker crumbs, sugar, and melted butter. Mix until the crumbs are evenly coated.
Press the crumb mixture firmly into the bottom of the springform pan to create an even crust. Bake for 10 minutes, then remove and let it cool.
In another bowl, beat the softened cream cheese with an electric mixer until smooth and creamy. Gradually add the sugar and vanilla, mixing until well combined.
Add the eggs, one at a time, mixing on low speed after each addition until just combined. Avoid overmixing.
Fold in the sour cream and fresh blackberries gently with a rubber spatula.
Pour the cheesecake filling over the cooled crust and smooth the top with the spatula.
Bake the cheesecake in the preheated oven for 50-60 minutes, or until the center is set but still slightly jiggly.
Turn off the oven and crack the oven door, allowing the cheesecake to cool slowly for 1 hour.
Refrigerate the cheesecake for at least 4 hours, or overnight, before removing it from the springform pan.
Garnish with additional fresh blackberries before serving if desired.