In a mixing bowl, combine the graham cracker crumbs, melted butter, and sugar until well mixed. Press this mixture firmly into the bottom of a 9-inch springform pan.

In a large mixing bowl, beat the cream cheese with an electric mixer on medium speed until smooth and fluffy, about 2 minutes. Gradually add in the sugar and vanilla extract, mixing well. Gently fold in the chopped pistachios and fresh raspberries until evenly distributed.

Carefully pour the creamy filling over the prepared graham cracker crust, smoothing the top with an offset spatula.

Preheat your oven to 325°F (163°C) and bake for approximately 40 minutes, until the edges are set but the center remains slightly jiggly.

Once the baking time is up, turn off the oven and crack the door open slightly. Allow the cheesecake to cool in the oven for about 1 hour.

Transfer to the refrigerator and let it chill for at least 4 hours, or overnight for best results.

To serve, release the cheesecake from the springform pan and garnish with extra raspberries and chopped pistachios.