Preheat the oven to 350°F and wrap the outside of a 9-inch springform pan with two layers of heavy-duty foil. Mix the graham cracker crumbs, ground pistachios, sugar and melted butter, press into the bottom of the pan and bake for 10 minutes.
Let the crust cool, reduce the oven to 325°F and bring a kettle of water to a boil. Blend the cottage cheese in a food processor or blender for 2 to 3 minutes, scraping down the sides, until completely silky and smooth.
Add the cream cheese, Greek yogurt, pistachio cream, sugar, cornstarch, vanilla, almond extract and salt, then blend until smooth. Add the eggs and pulse just until combined.
Pour the filling over the crust and tap the pan to release air bubbles. Set the springform in a roasting pan, add hot water about 1 inch up the sides and bake for 60 to 70 minutes, until the edges are set and the center jiggles slightly.
Turn off the oven, crack the door and let the cheesecake cool inside for 1 hour. Remove it from the water bath, loosen the edge with a thin spatula and let it cool completely at room temperature.
Refrigerate the cheesecake for at least 8 hours or overnight until firm.
Warm the pistachio cream in the microwave for 10 to 15 seconds so it drizzles easily. Release the springform ring, drizzle the pistachio cream over the top and finish with chopped pistachios and crushed freeze-dried raspberries.