MAKE THE CRUST: In a medium bowl, mix the crushed biscuits, melted butter, and sugar until evenly combined. Press the mixture firmly into the bottom of a 9-inch (23 cm) springform pan using the back of a spoon or flat-bottomed glass. Refrigerate while preparing the filling.
BLOOM THE GELATIN: In a small bowl, sprinkle the gelatin over cold water and let it sit for 5 minutes until spongy. Microwave for 10 to 15 seconds until completely dissolved, then set aside to cool slightly.
WHIP THE CREAM: In a large bowl, whip the heavy cream until soft peaks form. Place the whipped cream in the refrigerator to keep cold.
PREPARE THE CREAM CHEESE FILLING: In another bowl, beat the cream cheese until smooth. Add pistachio paste, powdered sugar, and vanilla extract, then mix until fully combined and creamy. Stir in the dissolved gelatin and mix well. Gently fold in the whipped cream with a spatula, maintaining as much air as possible in the mixture.
ASSEMBLE AND CHILL: Pour the pistachio filling over the prepared crust and smooth the surface with an offset spatula. Tap the pan gently on the counter to release air bubbles. Cover and refrigerate for at least 6 hours or overnight until fully set.
DECORATE AND SERVE: Once set, run a thin knife around the edge of the cheesecake before releasing the springform ring. Garnish the top with chopped pistachios and drizzle with pistachio cream or melted white chocolate if using. Slice with a sharp knife and serve chilled.