01 - Preheat oven to 340°F (170°C).
02 - In a bowl, combine crushed graham crackers, melted butter, finely chopped pistachios, and sugar. Mix until evenly moistened. Firmly press the mixture into the base of a 9-inch (23 cm) springform pan. Bake for 10 minutes, then set aside to cool.
03 - In a large mixing bowl, beat cream cheese and sugar with an electric mixer until smooth and creamy. Incorporate eggs one at a time, blending thoroughly between each addition.
04 - Add sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract to the batter. Beat until the mixture is uniform and silky. Gently fold in the roughly chopped pistachios.
05 - Pour the cheesecake filling over the cooled crust. Smooth the surface and gently tap the pan on the counter to release any air bubbles. Bake for 60 minutes, or until the center is almost set but still slightly wobbly.
06 - Run a thin knife around the edge to loosen. Allow cheesecake to cool completely in the pan, then cover and refrigerate for at least 4 hours, preferably overnight, to set.
07 - In a saucepan over medium heat, combine pitted cherries, sugar, and lemon juice. Stir occasionally until cherries begin to release juices. Dissolve cornstarch in water, then stir into the cherries. Simmer, stirring frequently, until the topping thickens. Remove from heat and cool completely.
08 - Remove chilled cheesecake from the springform pan. Spoon cooled cherry topping generously over the surface. Garnish with additional pistachios if desired. Slice and serve well-chilled.