01 - Set oven to 340°F and allow to fully preheat.
02 - In a bowl, mix crushed graham crackers, melted butter, chopped pistachios, and sugar until evenly combined. Firmly press mixture into the bottom of a 9-inch springform pan. Bake for 10 minutes, then let cool completely.
03 - Beat cream cheese and sugar with an electric mixer until smooth and fluffy. Add eggs one at a time, mixing thoroughly after each.
04 - Blend in sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until smooth. Gently fold in chopped pistachios.
05 - Pour the cream cheese filling over the cooled crust, smoothing the surface. Lightly tap the pan to release air bubbles. Bake for 60 minutes, or until just set in the center with a slight wobble. Run a knife around the edge, cool completely in the pan.
06 - Refrigerate the cheesecake in the pan for at least 4 hours, preferably overnight, to allow it to firm.
07 - Combine cherries, sugar, and lemon juice in a medium saucepan set over medium heat. Cook until cherries release their juice. Dissolve cornstarch in water and stir into cherries. Simmer until thickened, then let cool fully.
08 - Release cheesecake from the pan. Spoon cooled cherry topping evenly over the surface. Garnish with additional pistachios if desired. Slice and serve well-chilled.