Lightly dampen a 9 x 5-inch loaf pan so the parchment stays in place. Line it with two crossed parchment strips, leaving at least 3 inches of overhang on every side for lifting. Smooth the paper firmly into the corners to prevent deep creases in the cake. Clear a level space in a refrigerator set to 4°C or colder before beginning the filling.
Place the cold water in a small heatproof bowl and sprinkle the powdered gelatin evenly over the surface instead of pouring it into one mound. Leave it undisturbed for 5 minutes, until every granule looks hydrated and the mixture resembles a thick gel. Warm it over barely simmering water or in 5-second microwave intervals, stirring between intervals, just until clear and fluid. Do not boil it. Set aside briefly while preparing the mascarpone base.
In a large bowl, beat the cold mascarpone with an electric mixer on low speed for about 20 seconds, just until smooth. Add the pistachio paste, confectioners' sugar, vanilla, salt, and 100 g of the cold cream. Mix on low, then medium-low, until evenly green and free of visible mascarpone lumps, about 45 seconds. Whisk two spoonfuls of this mixture into the fluid gelatin, then stream that tempered gelatin back into the bowl while mixing on low.
Pour the remaining 500 g cold cream into a clean medium bowl. Whip at medium speed until the whisk leaves defined tracks and the cream forms medium peaks that hold their shape but curl slightly at the tips, about 2 to 4 minutes. Fold one-third into the pistachio base with a flexible spatula to loosen it. Fold in the remainder in two additions, rotating the bowl and scraping underneath, until no white streaks remain and the filling holds soft mounds.
Spread about one-fifth of the pistachio filling across the bottom of the lined pan, pushing it into the corners with an offset spatula. Add a single layer of graham crackers, breaking pieces to fit and leaving as few gaps as possible. Repeat until there are five filling layers and four cracker layers, finishing with filling. Press each cracker layer gently into contact with the cream without compacting it. Smooth the top, cover the pan, and refrigerate for at least 8 hours or up to 24 hours.
Check that the cake feels firm when pressed lightly and that a thin knife inserted near the center meets tender layers rather than crisp crackers. Use the parchment overhang to lift the cold cake onto a serving board, peeling the paper away carefully. Scatter the chopped roasted pistachios over the top and press them lightly into the cream. Cut into 10 slices with a serrated knife, wiping the blade between cuts, and serve while thoroughly chilled.
