Preheat oven to 325°F.
Mix crumbs, sugar, and butter for crust.
Press crust mixture into springform pan bottom.
Bake crust for 10 minutes. Let cool.
Beat cream cheese until smooth and fluffy.
Add sugar, mix until well combined.
Add eggs one at a time, mixing gently.
Stir in vanilla and sour cream.
Pour filling over prepared crust.
Bake cheesecake for 50 minutes.
Let cheesecake cool on wire rack.
For peaches, cook with sugar, lemon, cornstarch.
Simmer until peaches are thickened. Cool slightly.
Make cobbler topping with flour, sugar, butter, cinnamon.
Crumble topping mixture over peaches.
Bake peach topping for 15 minutes.
Spoon peach mixture over cheesecake top.
Chill cheesecake for 4 hours before serving.