Preheat the oven to 350°F.
Crush the graham crackers into fine crumbs in a food processor.
Add the melted butter and sugar to the graham cracker crumbs. Mix until the crumbs are evenly coated and resemble damp sand.
Press the crust mixture firmly into the bottom of a 9-inch springform pan and about ½ inch up the sides. Use the bottom of a flat glass to pack it down evenly.
Bake the crust for 8 minutes, then remove it from the oven.
Place a large roasting pan, or another large oven-safe pan, on the middle rack of the oven. Fill it with about 1 inch of water.
Reduce the oven temperature to 300°F.
Wrap the outside of the springform pan with aluminum foil, making sure the foil comes most of the way up the sides. Use extra-wide foil and double wrap it if needed to keep water from seeping into the crust.
In the bowl of a stand mixer, beat the cream cheese until smooth. Scrape down the sides of the bowl with a rubber spatula.
Add the sugar, sour cream, extracts, and salt. Mix until smooth and combined.
Add the dry pistachio pudding mix and mix until incorporated.
Add the eggs and beat on low speed only until fully mixed in. Do not overmix once the eggs are added.
Pour the pistachio cheesecake batter into the prepared crust and smooth the top.
Carefully place the foil-wrapped springform pan into the water bath.
Bake at 300°F for 1 hour 15 minutes, or until the edges are set and the center still has a slight jiggle.
Turn the oven off and leave the cheesecake inside for 30 minutes.
Crack the oven door and let the cheesecake rest inside for another 1 hour.
Carefully remove the cheesecake from the water bath and place it on the counter to cool for 1 hour.
Transfer the cheesecake to the refrigerator and chill for at least 8 hours, or overnight.
To make the sour cream icing, whisk the heavy cream until stiff peaks form.
Add the sour cream and powdered sugar. Whisk until smooth and combined.
After the cheesecake has chilled, run a thin knife under hot water, then carefully run it around the edge of the cheesecake.
Release the springform pan.
Scoop the sour cream icing onto the center of the cheesecake and spread it evenly over the top, stopping just before the edge.
Sprinkle chopped pistachios over the icing.
Return the cheesecake to the refrigerator for 15 to 20 minutes to let the icing set slightly, then slice and serve chilled.