Preheat your oven to 325°F (163°C). Prepare a 9-inch springform pan by greasing the sides and bottom lightly.
In a mixing bowl, combine the graham cracker crumbs, 1/3 cup granulated sugar, and melted butter until the mixture resembles wet sand.
Press the crumb mixture firmly into the bottom of the prepared springform pan to form an even base. Bake in the preheated oven for 10 minutes, then remove and let cool while you prepare the filling.
In a large bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth and creamy, about 2-3 minutes.
Gradually add 1 cup of granulated sugar to the cream cheese, beating until well combined. Scrape down the sides of the bowl as necessary.
Add the sour cream, finely ground pistachios, pistachio pudding mix, vanilla extract, and almond extract. Mix on low speed until everything is well incorporated and smooth.
Pour the cheesecake filling over the cooled crust, smoothing the top with a spatula.
Bake in the oven for 55-60 minutes, or until the edges are set but the center still has a slight jiggle.
Turn off the oven and crack the door open, allowing the cheesecake to cool in the oven for about 1 hour. This helps prevent cracking.
Once cooled, refrigerate the cheesecake for at least 4 hours, preferably overnight, to let it set fully.
Before serving, sprinkle the top with chopped pistachios for a beautiful garnish.