Preheat oven to 325°F (160°C). Wrap the outside of a 9-inch springform pan with a double layer of heavy-duty aluminum foil if using a water bath, or grease the pan well if skipping the bath.

In a bowl, combine graham cracker crumbs, chopped toasted pistachios, sugar, melted butter, and a pinch of salt. Press the mixture firmly into the bottom (and slightly up the sides if you like) of the springform pan. Chill in the fridge while you make the filling.

In a small saucepan, combine raspberries, sugar, and lemon juice. Cook over medium heat, stirring, until raspberries break down, about 5–7 minutes. If you prefer a thicker coulis, stir in the cornstarch slurry and cook 1–2 more minutes. Let cool, then strain through a sieve if you want a seedless sauce. Chill.

Beat the room-temperature cream cheese on medium-low speed until smooth and lump-free (about 2 minutes). Add sugar and beat until combined. Mix in sour cream, vanilla, and lemon zest. Add eggs one at a time, mixing gently and stopping as soon as each is incorporated to prevent overbeating. Stir in heavy cream and scrape the bowl clean.

Pour half the filling over the chilled crust and smooth. Spoon half the raspberry sauce in dots over the filling and gently swirl with a knife. Pour the remaining filling, then add remaining raspberry sauce and swirl again lightly for pretty marbling.

If using a water bath, place the wrapped springform in a larger pan and pour hot water about halfway up the sides of the springform. Bake at 325°F for 50–65 minutes, until the edges are set and the center jiggles slightly. Turn off the oven, crack the door, and let cheesecake sit in the warm oven for 45 minutes to help prevent cracks.

Remove from the oven and cool to room temperature on a wire rack. Refrigerate for at least 6 hours, preferably overnight.

In a food processor, pulse chopped toasted pistachios with brown sugar and a pinch of salt until crumbly. Cut in the cold butter with a fork or pulse briefly until coarse crumbs form. Optionally, toast these crumbs in a skillet for 2–3 minutes for extra flavor, stirring constantly. Cool completely.

Run a thin knife around the pan, release the springform, and transfer cheesecake to a serving plate. Sprinkle pistachio crumb on top and press gently to adhere. Garnish with extra whole raspberries and a light dusting of powdered sugar if desired.