Preheat oven to 350°F (175°C). Mix crushed crackers or biscuits with sugar and melted butter until moist.
Press mixture firmly into bottom and slightly up the sides of a 9-10 inch springform pan.
Bake crust for 8-10 minutes then set aside to cool.
In a large bowl, beat softened cream cheese with sugar until smooth and creamy.
Add eggs one at a time, mixing gently after each addition.
Blend in sour cream, vanilla extract, and lemon zest until fully combined.
Pour filling over cooled crust and smooth the top.
Bake cheesecake for 45-55 minutes, until edges are set and center slightly jiggles.
Turn off oven, leave cheesecake inside with door slightly open for 1 hour.
Cool completely at room temperature, then refrigerate for at least 4 hours or overnight.
In a saucepan, cook cherries with sugar and lemon juice over medium heat until softened, about 5-7 minutes.
Stir in cornstarch slurry and cook until topping thickens, then cool.
Spread cherry topping over chilled cheesecake and sprinkle chopped pistachios on top.
Slice and serve with extra cherries or whipped cream if desired.