To a stand mixer fitted with a paddle attachment, add cream cheese and sugar, beating on medium-low speed until smooth. Add sour cream, pistachio paste, lemon zest, lemon juice, and salt, and continue to mix on low speed until fully incorporated.
Add eggs one at a time, beating between each addition and scraping down the sides of the bowl as you go. Mix until just combined.
Pour the cheesecake mixture into the prepared baked crust and smooth the top. Tap the pan on a flat surface to remove any air bubbles. Place the cheesecake in a large roasting pan and carefully pour the boiling water ½ the way up the springform pan.
Bake for 55-65 minutes or until the edges are set, and the center is slightly jiggly.
Turn the oven off and prop the door open slightly, allowing it to slowly cool down for about 1 hour. Then, remove the pan from the water and oven, remove the foil, and place on a wire rack to cool completely. Once cooled to room temperature, cover with plastic wrap and refrigerate for at least 8 hours or overnight.
Gently run a knife around the edges of the pan and carefully release the ring of your springform pan. Run the knife between the crust and bottom pan and use a spatula to carefully lift the cheesecake to a serving plate. Cut into 12 equal slices and serve cold. Garnish with crushed pistachios.