01 - Preheat oven to 340°F (170°C) with rack in the middle position.
02 - In a bowl, combine crushed graham crackers, melted butter, chopped pistachios, and sugar until mixture resembles wet sand.
03 - Press crust mixture firmly into the base of a 9-inch springform pan. Bake for 10 minutes until set, then allow to cool to room temperature.
04 - In a large mixing bowl, beat cream cheese and granulated sugar on medium speed until smooth and airy. Add eggs one at a time, mixing thoroughly after each addition.
05 - Blend in sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until the batter is homogeneous. Fold in the chopped pistachios evenly.
06 - Pour cheesecake filling over the cooled crust, smoothing the surface. Tap the pan gently to remove any trapped air bubbles.
07 - Bake in the oven for 60 minutes, or until the center is just set yet slightly wobbly. Remove and run a knife around the edge to loosen. Cool in pan, then chill for a minimum of 4 hours or overnight.
08 - In a small saucepan, combine cherries, sugar, and lemon juice. Heat over medium until cherries release their juices. Dissolve cornstarch in water and stir into cherry mixture. Simmer until glossy and thickened. Cool completely.
09 - Once fully chilled, remove cheesecake from the springform pan. Top with cooled cherry sauce and garnish with additional pistachios if desired. Slice and serve cold.