01 - Preheat oven to 340°F (170°C). Position rack in the center.
02 - Combine graham cracker crumbs, melted butter, finely chopped pistachios, and sugar in a large bowl. Press mixture firmly into the base of a 9-inch (23 cm) springform pan. Bake for 10 minutes until just set and fragrant. Let cool completely.
03 - In a mixing bowl, beat cream cheese and granulated sugar with an electric or stand mixer until creamy and smooth. Add eggs one at a time, blending thoroughly after each addition.
04 - On low speed, incorporate sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract. Gently fold in chopped pistachios with a rubber spatula.
05 - Pour the cheesecake filling over the cooled crust. Smooth the top with a spatula and tap the pan gently to release air bubbles. Bake for 60 minutes, or until the center is set but the middle still jiggles slightly.
06 - Run a thin knife around the edge of the cake while warm to loosen. Let the cheesecake cool in the pan at room temperature, then refrigerate for at least 4 hours or overnight until fully set.
07 - In a saucepan, combine cherries, sugar, and lemon juice. Cook over medium heat until cherries release juices. In a small bowl, dissolve cornstarch in water and add to the cherry mixture. Simmer, stirring constantly, until thickened. Remove from heat and allow to cool completely.
08 - Once cheesecake is thoroughly chilled, remove from the springform pan. Spoon cherry topping evenly over the surface. Garnish with additional pistachios if desired. Slice with a clean knife and serve chilled.