Put your pistachios in a food processor and pulse until they are coarsely chopped.
Add the graham crackers, sugar, and salt. Blitz until the crackers are fine crumbs and there are no more big pieces.
Melt the butter in the microwave and pour it into the food processor, pulse until it looks like wet sand. You might not need all of the butter so try with ¾ of it first, then gradually add a little more if needed. When it's ready it should be able to clump together when squeezed in your hands.
Tip the crumb mixture into your loose-bottomed pan and use your hands, or the bottom of a glass, to press it down to make a compacted, even layer across the bottom and slightly up the sides of the pan.
Bake it in the preheated oven for 10 minutes, just to help set the base. Remove and let it cool slightly while you make the cheesecake.
Make the Pistachio Cheesecake
Turn the oven temperature down to 325°F / 170°C and prepare your cheesecake pan for a water bath. (See notes).
Beat the cream cheese, sugar, and cornstarch together in a bowl until creamy and free of lumps. You can use a mixer or do it by hand.
Add the eggs, egg yolk, vanilla, and almond extract and beat them in until combined. Don't overmix, just enough to incorporate.
Add the pistachio paste and mix it in until it is incororated.
Drizzle in the cream, a little at a time, and mix it in gradually.
Pour the cheesecake batter into your prepared cake pan and place in a waterbath in the oven. (I like to get my pan positioned in the roasting dish on the oven shelf first, then pour in the water - this stops the water from sloshing around when being put in the oven).
Bake for 45 minutes or until the cheesecake is baked. When it's ready, the outer 2-3 inches of cheesecake should be firm and set, but the middle should still have a slight jiggle. If it still looks liquidy in the middle, do not take it out yet, it will be underbaked and will fall apart when you remove it from the pan! See blog post above for more details on how to know when it's ready.
Once it's ready, turn the oven off and crack the oven door open slightly. Leave the cheesecake in there for an hour, then remove it from the oven and the water bath and let it continue to cool on the countertop.
Once it has completely cooled, transfer it to the fridge to set for at least 4 hours, preferably overnight.
Decorate
Once the cheesecake has totally chilled, remove it from the cake pan.
Spread an even layer of pistachio cream on top and sprinkle with chopped pistachios.
Notes
Please note, pistachio paste and pistachio cream are two different ingredients. Pistachio Paste is just made with 100% pistachios, blended into a nut butter. You can buy it online, or you can make your own if you have a powerful food processor. I have a blog post all about how to make your own pistachio paste.Pistachio Cream is a sweet, spreadable topping made using pistachios, white chocolate, butter and milk. You can make your own but I actually found the best results with the storebought pistachio cream, specifically Pisti Pistachio Cream.
Other Ingredient Notes
The cream should be heavy cream, heavy whipping cream or double cream. Anything less than 35% fat content will not be thick enough. Likewise, you should use full-fat cream cheese.
How to Prepare a Pan for a Water Bath
You need to seal the base of your loose-bottomed pan so it will be watertight. The classic way is to wrap the pan in multiple layers of foil to create a seal. My new favorite hack is that I bought a silicone cake pan the same size, or slightly larger than my cake pan and just put the cake pan inside. Not a drop of water will get in and your cheesecake crust will be completely free of soggy bottoms!