Preheat your oven to 325°F (163°C). Line the baking dish with parchment paper, leaving some overhang for easy removal later.
In a mixing bowl, combine the graham cracker crumbs, melted butter, ¼ cup sugar, and a pinch of salt. Mix until well combined. Press this mixture into the bottom of the lined baking dish to form a crust. Bake in the preheated oven for 10 minutes and then let it cool slightly.
In another mixing bowl, beat the softened cream cheese and 1 cup sugar with an electric mixer until smooth and creamy.
Add the eggs one at a time, mixing well after each addition. Then, add in the vanilla extract and sour cream, mixing until it's fully incorporated.
Gently fold in the flour into the cream cheese mixture until just combined. Be careful not to overmix.
Pour half of the cheesecake batter over the cooled crust.
Evenly distribute the blackberries over the cheesecake layer. Pour the remaining cheesecake batter on top and smooth it out with a spatula.
Sprinkle the chopped pistachios on top of the cheesecake batter.
Bake in the oven for 30 minutes or until the center is set but still slightly jiggly.
Remove from the oven and let it cool to room temperature before refrigerating for at least 2 hours to set completely.
Once set, lift the cheesecake out of the pan using the parchment overhang, slice into bars, and serve.