01 - Preheat oven to 340°F (170°C).
02 - Combine crushed graham crackers, melted butter, finely chopped pistachios, and sugar. Press mixture firmly into the bottom of a 9-inch (23 cm) springform pan. Bake for 10 minutes. Let cool completely.
03 - In a large mixing bowl, beat cream cheese and sugar using an electric mixer until smooth and fluffy. Add eggs one by one, mixing thoroughly after each addition.
04 - Mix in sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until fully blended. Gently fold in roughly chopped pistachios.
05 - Pour filling over the cooled crust and smooth the surface. Gently tap the pan to remove air bubbles. Bake for 60 minutes, or until the center is nearly set but slightly wobbly. Run a thin knife around the edge to loosen. Allow to cool in the pan before transferring to the refrigerator.
06 - Refrigerate for at least 4 hours, preferably overnight, to allow the cheesecake to set fully.
07 - In a small saucepan, gently heat cherries, sugar, and lemon juice over medium heat until cherries begin to release their juices. Dissolve cornstarch in water, then stir into the pan. Simmer until the mixture thickens. Remove from heat and cool completely.
08 - Release the chilled cheesecake from the pan. Spread cherry topping evenly over the surface. Garnish with extra pistachios if desired. Slice and serve chilled.