Make the crust: Preheat your oven to 325°F (163°C). In a medium bowl, combine the graham cracker crumbs, sugar, and melted butter. Press this mixture into the bottom of a 9-inch springform pan to form a crust. Bake for 8-10 minutes, then set aside to cool.

1. Prepare the cheesecake filling: In a large mixing bowl, beat the softened cream cheese and sugar together until smooth and creamy. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract and sour cream. Pour the cheesecake batter over the cooled graham cracker crust.
2. Make the peach topping: In a separate bowl, combine the sliced peaches, sugar, cinnamon, and cornstarch (if using). Stir gently to combine and set aside.
3. Prepare the crumble topping: In another bowl, mix the flour, oats, brown sugar, cinnamon, and salt. Cut in the cold butter using a pastry cutter or your hands until the mixture resembles coarse crumbs.
4. Assemble the cheesecake: Spoon the peach topping over the cheesecake layer, then sprinkle the crumble topping over the peaches.
5. Bake the cheesecake: Place the cheesecake in the oven and bake for 55-60 minutes, or until the center is set and the top is golden brown. The cheesecake may have a slight jiggle in the center, but it will firm up as it cools.
6. Cool and chill: Allow the cheesecake to cool completely at room temperature, then refrigerate for at least 4 hours, preferably overnight.
7. Serve: Once chilled, remove the cheesecake from the springform pan and transfer to a serving platter. Slice and serve!