01 - Set oven to 340°F (170°C) to begin warming for even baking.
02 - Combine crushed graham crackers, melted butter, finely chopped pistachios, and sugar in a mixing bowl. Press the mixture evenly into the base of a 9-inch springform pan. Bake for 10 minutes, then transfer to a rack to cool completely.
03 - In a clean mixing bowl, beat cream cheese and sugar with an electric or stand mixer until creamy and smooth. Add eggs one at a time, mixing thoroughly after each addition. Fold in sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until fully combined. Gently mix in the chopped pistachios.
04 - Pour the prepared filling over the cooled crust. Smooth the surface with a spatula. Tap the pan gently to remove any trapped air bubbles. Bake for approximately 60 minutes, until the center is just set with a slight wobble. Run a knife around the edge to loosen, then cool completely in the pan.
05 - Refrigerate the cheesecake for at least 4 hours, preferably overnight, to allow for full setting and flavor development.
06 - In a saucepan, cook cherries, sugar, and lemon juice over medium heat until juices are released. In a separate bowl, dissolve cornstarch in cold water, then stir into the cherry mixture. Simmer until thickened. Remove from heat and allow to cool completely.
07 - Release the chilled cheesecake from the springform pan. Spoon the cherry topping evenly over the surface. Garnish with extra pistachios if desired. Slice with a sharp knife and serve chilled.