01 - Preheat the oven to 340°F (170°C).
02 - In a bowl, combine crushed graham crackers, melted butter, chopped pistachios, and sugar. Press the mixture firmly into the base of a 9-inch springform pan. Bake for 10 minutes, then cool completely.
03 - Beat cream cheese and sugar with an electric mixer until smooth and fluffy. Add eggs one at a time, mixing well after each addition.
04 - Blend in sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until thoroughly combined. Gently fold in chopped pistachios.
05 - Pour the mixture over the cooled crust and smooth the surface. Gently tap the pan to release any air bubbles.
06 - Bake for 60 minutes, or until the center is just set but still slightly wobbly. Run a knife around the edge and allow to cool in the pan. Refrigerate for at least 4 hours or overnight.
07 - In a saucepan, combine cherries, sugar, and lemon juice. Cook over medium heat until the cherries release their juices. Dissolve cornstarch in water, stir into cherries, and simmer until thickened. Cool completely.
08 - Remove chilled cheesecake from the pan. Spoon cherry topping over the surface and garnish with extra pistachios if desired. Slice and serve chilled.