01 - Set oven temperature to 340°F (170°C).
02 - Combine crushed graham crackers, melted butter, chopped pistachios, and sugar in a mixing bowl. Press mixture firmly into the base of a 9-inch springform pan. Bake for 10 minutes, then allow to cool completely.
03 - Beat cream cheese and sugar with an electric mixer until smooth and fluffy. Add eggs one at a time, mixing thoroughly after each addition.
04 - Blend in sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until fully combined. Gently fold in chopped pistachios.
05 - Pour the cheesecake filling over the cooled crust. Smooth the top and tap the pan gently on the counter to remove air bubbles.
06 - Bake for 60 minutes, or until center is just set yet slightly wobbly. Run a thin knife around the edge, then cool in the pan. Chill in the refrigerator for at least 4 hours or preferably overnight.
07 - Combine cherries, sugar, and lemon juice in a saucepan over medium heat. Once juices are released, mix cornstarch with water and stir into the cherries. Simmer until topping thickens, then cool completely.
08 - Release cheesecake from pan. Spoon the cooled cherry topping over the surface. Garnish with extra pistachios if preferred. Slice and serve well chilled.