Preheat your oven to 325°F (163°C) while you grease a 9-inch springform pan. In a mixing bowl, combine graham cracker crumbs, melted butter, and granulated sugar until the mixture holds together. Press this crumb mixture evenly into the bottom of your prepared pan to form a solid, compact crust. Bake for 10 minutes or until lightly golden, then set aside to cool.

In a large mixing bowl, use an electric mixer to beat the cream cheese and granulated sugar until smooth and creamy, which takes about 2-3 minutes. Add in the vanilla extract and continue mixing until well combined. Incorporate the eggs one at a time, beating just until combined after each addition. Next, gently mix in the sour cream, heavy cream, and flour until no lumps remain, being careful not to overmix.

Once your cheesecake filling is smooth, gently fold in the fresh raspberries and crushed pistachios using a spatula. Make sure not to overmix.

Pour the cheesecake filling over the pre-baked crust in your springform pan, spreading it evenly. Bake in the preheated oven for about 55-60 minutes, or until the edges are set but the center still has a slight jiggle. Once baked, remove it from the oven and let it cool completely at room temperature before transferring it to the refrigerator.

Once your cheesecake is thoroughly cooled, spread raspberry mousse gently over the top of the cheesecake layer. Chill the cheesecake in the refrigerator for at least 2 hours to allow the mousse to firm up.

In a chilled mixing bowl, whip the heavy cream with powdered sugar and an additional teaspoon of vanilla extract until stiff peaks form. Once whipped, either pipe or spread the whipped cream over the raspberry mousse layer of the cheesecake.

Garnish your Pistachio Raspberry Cheesecake with fresh raspberries and a sprinkle of crushed pistachios on top. Refrigerate the cheesecake for at least 4 hours, or preferably overnight, for the best flavor and set.