01 - Set oven temperature to 340°F (170°C) for even baking.
02 - In a mixing bowl, combine crushed graham crackers, melted butter, chopped pistachios, and sugar. Mix until evenly blended.
03 - Press crust mixture firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes, then allow to cool to room temperature.
04 - In a large bowl, beat cream cheese and granulated sugar with a mixer until smooth and fluffy. Add eggs one at a time, beating well after each addition.
05 - Stir in sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until fully integrated. Gently fold in chopped pistachios.
06 - Pour the prepared filling over the cooled crust. Smooth the surface and tap the pan lightly to release any trapped air bubbles.
07 - Bake for 60 minutes, or until center is set but slightly wobbly. Run a thin knife around the edge to loosen, then cool in the pan.
08 - Refrigerate uncovered for at least 4 hours, ideally overnight, to allow filling to set completely.
09 - In a saucepan, combine cherries, sugar, and lemon juice. Cook over medium heat until cherries begin releasing juice. Dissolve cornstarch in water; add to the cherries and simmer until mixture thickens. Let cool completely.
10 - Remove fully chilled cheesecake from pan. Spread cooled cherry topping evenly on top. Garnish with additional pistachios if desired. Slice and serve chilled.