Preheat the oven to 325°F (163°C).
In a food processor, pulse the pistachios until finely ground but not pasty.
Combine the ground pistachios, graham cracker crumbs, 1/2 cup sugar, and melted butter in a medium bowl. Mix until well combined.
Press the crust mixture firmly into the bottom of a 9-inch springform pan to form an even layer.
Bake the crust for 10 minutes, then remove from the oven and set aside to cool slightly.
In a large mixing bowl, beat the softened cream cheese with 1 cup sugar and vanilla extract until smooth and creamy using an electric mixer.
Add the eggs one at a time, mixing well after each addition.
Mix in the sour cream until fully incorporated.
In a small saucepan, combine the fresh raspberries, 1/4 cup sugar, and lemon juice. Cook over medium heat for 5-7 minutes, stirring occasionally, until the raspberries break down and the mixture thickens slightly.
Strain the raspberry sauce through a fine mesh sieve to remove seeds, then let it cool to room temperature.
Pour half of the cheesecake batter over the baked crust in the springform pan.
Drizzle half of the raspberry sauce over the batter, then use a knife or skewer to gently swirl the sauce into the batter.
Pour the remaining cheesecake batter over the swirled layer, then drizzle the remaining raspberry sauce on top and swirl again.
Bake the cheesecake for 55-60 minutes, or until the edges are set and the center is slightly jiggly.
Turn off the oven and leave the cheesecake inside with the door slightly open for 1 hour to cool gradually.
Remove the cheesecake from the oven and refrigerate for at least 4 hours or overnight to fully set.
Before serving, sprinkle the chopped pistachios evenly over the top of the cheesecake.
Carefully remove the sides of the springform pan and slice the cheesecake to serve.