Preheat oven to 325°F (163°C). Grease a springform pan.
Mix graham crumbs, melted butter, sugar, and cinnamon. Press into pan and bake 8–10 minutes. Let cool.
Beat cream cheese and sugar until smooth. Add eggs one at a time, then vanilla and sour cream.
Pour cheesecake mixture over crust.
In a saucepan, cook peaches, brown sugar, cinnamon, cornstarch, lemon juice, vanilla, and butter for 5–7 minutes until thick.
Spoon peach mixture over cheesecake layer.
Bake 45–55 minutes until center is slightly set.
Turn off oven and let cool inside for 1 hour.
Chill in refrigerator at least 4 hours before serving.
Top with whipped cream or caramel if desired.