Preheat the oven to 325°F (163°C).
In a medium bowl, combine the graham cracker crumbs, 1/4 cup granulated sugar, and melted butter. Stir until the mixture resembles wet sand.
Press the crumb mixture firmly into the bottom of a 9-inch springform pan to form an even crust layer.
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 an electric mixer on medium speed until smooth and creamy, about 3 minutes.
Add 1 cup granulated sugar and vanilla extract to the cream cheese and beat until combined.
Add the eggs one at a time, beating on low speed after each addition just until incorporated. Do not overmix.
Add the sour cream and flour, and mix on low speed until just combined.
Pour the cheesecake batter over the cooled crust in the springform pan and smooth the top with a spatula.
Bake the cheesecake for 60 to 70 minutes, or until the edges are set and the center is slightly jiggly but not liquid.
Turn off the oven and crack the oven door open. Let the cheesecake cool in the oven for 1 hour.
Remove the cheesecake from the oven and refrigerate for at least 4 hours, preferably overnight.
While the cheesecake chills, prepare the cherry compote: In a small saucepan, combine the cherries, 1/3 cup granulated sugar, and lemon juice.
In a small bowl, mix the cornstarch and water until smooth, then add to the saucepan.
Cook the cherry mixture over medium heat, stirring constantly, until it thickens and the cherries soften, about 5 to 7 minutes.
Remove the compote from heat and let it cool to room temperature.
Before serving, spread the cherry compote evenly over the top of the chilled cheesecake.
Sprinkle the toasted and chopped pistachios over the cherry topping.
Carefully remove the sides of the springform pan and slice the cheesecake to serve.