Preheat the oven to 350 F. Spread all the pistachios onto a baking pan and bake for 10 minutes, shaking the pan halfway for even heating.
Separate the nuts into two bowls, into one add 100g of pistachios (this will be for the crust) and into the other 127g (this is for the filling and optionally for the whipped cream).
First process the nuts for the crust, blend them on high until you have a pistachio flour, it should look like almond flour, the nuts being in little bits. Transfer back into the bowl and let cool.
Add the nuts for the filling (127g) into the food processor and this time we’re going to process on high until we have a loose paste. This can take up to 30 minutes depending on your food processor and may require scraping the bowl a few times. Once you can stir the paste and it easily runs off the spoon when lifted, it’s done. Set aside to cool.
If making ahead of time, store both the ‘pistachio flour’ and ‘pistachio paste’ in an airtight container. The flour should be kept at room temperature, the paste in the fridge.