Preheat the oven to 325°F (163°C).
In a food processor, pulse the pistachios until finely ground but not pasty.
Combine the ground pistachios, graham cracker crumbs, 1/4 cup sugar, and melted butter in a bowl. Mix until evenly combined.
Press the mixture firmly into the bottom of a 9-inch springform pan to form an even crust.
Bake the crust for 10 minutes, then remove from the oven and set aside to cool.
In a large mixing bowl, beat the softened cream cheese with 1 cup sugar and vanilla extract until smooth and creamy.
Add the eggs one at a time, beating well after each addition.
Mix in the sour cream until fully incorporated.
Pour the cream cheese filling over the cooled crust in the springform pan.
Bake the cheesecake for 55 to 60 minutes, or until the center is almost set but still slightly jiggly.
Turn off the oven, crack the oven door, and let the cheesecake cool inside for 1 hour.
Remove the cheesecake from the oven and refrigerate for at least 4 hours or overnight.
While the cheesecake chills, prepare the cherry compote: In a small saucepan, combine the cherries, 1/3 cup sugar, and lemon juice.
Cook over medium heat until the cherries release their juices and the sugar dissolves, about 5 minutes.
In a small bowl, dissolve the cornstarch in water, then stir into the cherry mixture.
Cook, stirring constantly, until the mixture thickens, about 2 minutes.
Remove from heat and let cool to room temperature.
Once the cheesecake is chilled, spread the cherry compote evenly over the top.
Sprinkle the chopped pistachios over the cherry topping.
Carefully remove the sides of the springform pan before serving.
Slice and serve chilled.