01 - Preheat oven to 340°F (170°C).
02 - Mix crushed graham crackers, melted butter, finely chopped pistachios, and sugar until evenly combined. Press firmly into the base of a 9-inch springform pan. Bake for 10 minutes. Allow crust to cool completely.
03 - In a large mixing bowl, beat cream cheese and sugar using an electric or stand mixer until smooth and fluffy. Add eggs one at a time, fully incorporating after each addition.
04 - Blend in sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until mixture is uniform. Gently fold in roughly chopped pistachios.
05 - Pour filling over the cooled crust. Smooth the surface and tap the pan to remove air bubbles.
06 - Bake for 60 minutes, or until set but center remains slightly wobbly. Run a thin knife around the edge of the cheesecake to loosen. Cool in the pan, then refrigerate at least 4 hours or overnight.
07 - Combine pitted cherries, sugar, and lemon juice in a saucepan over medium heat. Cook until cherries begin releasing juice. In a small bowl, mix cornstarch and water. Stir into cherry mixture and simmer until thickened. Let cool completely.
08 - Remove chilled cheesecake from pan. Spoon cherry topping over cake before serving. Garnish with extra pistachios if desired. Slice and serve chilled.