Preheat the oven to 325°F (163°C).
In a food processor, combine the shelled pistachios, 1/4 cup granulated sugar, and salt. Pulse until the mixture resembles coarse crumbs.
Add the melted butter to the pistachio mixture and pulse until the crumbs are evenly moistened.
Press the pistachio crust mixture firmly into the bottom of a 9-inch springform pan to form an even layer.
Bake the crust in the preheated oven for 10 minutes. Remove and set aside to cool slightly.
In a large mixing bowl, beat the softened cream cheese with 1 cup granulated sugar until smooth and creamy.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract, sour cream, and all-purpose flour until just combined.
Pour the cream cheese filling over the cooled pistachio crust, smoothing the top with a spatula.
Bake the cheesecake for 55 minutes to 1 hour, or until the center is almost set but still slightly jiggly.
Turn off the oven and leave the cheesecake inside with the door slightly open for 1 hour.
Remove the cheesecake from the oven and cool completely at room temperature, then refrigerate for at least 3 hours or overnight.
While the cheesecake chills, prepare the cherry topping: In a small saucepan, combine the cherries, 1/4 cup granulated 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, mix the cornstarch and water until smooth, then add to the cherry mixture.
Cook and stir until the topping thickens, about 2 minutes. Remove from heat and let cool to room temperature.
Before serving, spread the cherry topping evenly over the chilled cheesecake.
Release the cheesecake from the springform pan and transfer to a serving plate.
Slice and serve chilled.