Preheat the oven to 325°F (163°C).
In a medium bowl, combine the finely chopped pistachios, graham cracker crumbs, 1/4 cup granulated sugar, and melted butter. Mix until the mixture resembles wet sand.
Press the pistachio mixture firmly into the bottom of a 9-inch springform pan to form an even crust 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 granulated sugar until smooth and creamy using an electric mixer on medium speed.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract, sour cream, and flour until just combined and smooth.
Pour the cream cheese filling over the cooled crust, smoothing the top with a spatula.
Bake the cheesecake for 55 to 60 minutes, or until the edges are set and the center is slightly jiggly but not liquid.
Turn off the oven and leave the cheesecake inside with the door slightly ajar for 1 hour.
Remove the cheesecake from the oven and cool to room temperature on a wire rack.
While the cheesecake cools, prepare the raspberry topping: In a small saucepan, combine the fresh raspberries, 1/4 cup granulated sugar, and lemon juice.
Cook over medium heat until the raspberries release their juice and the sugar dissolves, about 5 minutes.
In a small bowl, mix the cornstarch with cold water until smooth, then stir into the raspberry mixture.
Cook for another 2 minutes, stirring constantly, until the mixture thickens.
Remove from heat and let the raspberry topping cool completely.
Once the cheesecake is cooled to room temperature, spread the raspberry topping evenly over the top.
Refrigerate the cheesecake for at least 4 hours or overnight to set completely before serving.
Run a knife around the edges of the cheesecake before releasing the springform pan.
Slice and serve chilled.