Preheat your oven to 325°F (165°C).
In a bowl, combine graham cracker crumbs, melted butter, and sugar. Press this mixture into the bottom of a springform pan. Bake for 10 minutes, then let it cool.
In another bowl, beat the cream cheese and sugar together until smooth. Add the eggs one at a time, mixing well after each. Stir in sour cream and vanilla extract, then pour the filling over the crust.
Toss the diced peaches with brown sugar, cinnamon, and flour. Spoon this mixture over the cheesecake filling.
In a separate bowl, mix flour, brown sugar, butter, and cinnamon until crumbly. Sprinkle this over the peaches.
Bake for 60-70 minutes or until the center is set. Turn off the oven and let the cheesecake sit inside with the door slightly ajar for 1 hour.
Let the cheesecake cool completely before putting it in the fridge for at least 4 hours or overnight.
Slice and serve this creamy, sweet dessert with its perfect balance of spiced peaches and buttery crumble.