01 - Set oven temperature to 340°F (170°C).
02 - Mix crushed graham crackers, melted butter, finely chopped pistachios, and sugar in a bowl. Firmly press mixture into the base of a 9-inch springform pan. Bake for 10 minutes, then allow to cool completely.
03 - Beat cream cheese and granulated sugar with an electric mixer until smooth and fluffy. Add eggs one at a time, fully incorporating each before adding the next.
04 - Incorporate sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract into the batter. Gently fold in chopped pistachios.
05 - Pour cheesecake filling over cooled crust. Smooth the surface and tap the pan gently to release trapped air.
06 - Bake for 60 minutes, or until the center is just set with a slight wobble. Run a thin knife around the pan edge to loosen. Cool in the pan before refrigerating for at least 4 hours, preferably overnight.
07 - Combine cherries, sugar, and lemon juice in a saucepan. Heat over medium until cherries release juice. Dissolve cornstarch in water; stir into cherries and simmer until thickened. Let cool fully.
08 - Remove chilled cheesecake from pan. Spoon cooled cherry topping over the surface. Garnish with additional pistachios if desired. Slice and serve well-chilled.