01 - Preheat oven to 340°F (170°C).
02 - Mix crushed graham crackers, melted butter, finely chopped pistachios, and sugar. Press mixture firmly into the base of a 9-inch (23 cm) springform pan. Bake for 10 minutes. Allow to cool.
03 - On medium speed, beat cream cheese with sugar until completely smooth. Add eggs individually, blending well after each addition.
04 - Gently mix in sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until fully integrated. Fold in roughly chopped pistachios.
05 - Pour batter over cooled crust, spreading evenly. Tap pan lightly to dissipate air bubbles.
06 - Bake for 60 minutes, or until center is almost set with slight wobble. Run a knife around edge, then cool in pan. Refrigerate at least 4 hours, or overnight, to fully set.
07 - Combine cherries, sugar, and lemon juice in saucepan. Cook over medium heat until cherries release their juices. Dissolve cornstarch in water, stir into saucepan, and simmer until mixture thickens. Cool completely before use.
08 - Remove cooled cheesecake from pan. Top with cherry mixture. Garnish with additional pistachios as desired. Slice and serve chilled.