01 - Set oven temperature to 340°F. Allow oven to fully preheat before proceeding.
02 - Combine crushed graham crackers, melted butter, finely chopped pistachios, and sugar in a mixing bowl. Blend until evenly moistened. Press mixture firmly onto the bottom of a 9-inch springform pan to form an even layer. Bake for 10 minutes, then transfer to a wire rack to cool.
03 - In a large bowl, beat softened cream cheese together with granulated sugar using an electric mixer until smooth and creamy. Add eggs one at a time, ensuring each is incorporated thoroughly before adding the next.
04 - Blend in sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract. Mix until the batter is uniform and silky. Gently fold in roughly chopped pistachios, taking care not to overmix.
05 - Pour cream cheese filling over the cooled crust in the springform pan. Smooth the surface with a spatula, then gently tap the pan on the counter to release air bubbles. Bake for 60 minutes, or until the center is just set but still slightly wobbly when gently shaken.
06 - Run a thin knife around the edge of the baked cheesecake to prevent cracking. Allow cheesecake to cool completely at room temperature in the pan. Once cooled, refrigerate uncovered for at least 4 hours, ideally overnight, to fully set.
07 - In a saucepan over medium heat, combine cherries, sugar, and lemon juice. Cook until cherries release their juices, stirring occasionally. In a small bowl, dissolve cornstarch in water, then stir into cherries. Continue simmering until the topping thickens. Remove from heat and set aside to cool completely.
08 - Carefully remove chilled cheesecake from the springform pan. Spoon cherry topping over the surface, spreading evenly. Garnish with additional pistachios if desired. Slice with a sharp knife and serve cold.