Prepare the Crust: Preheat the oven to 325°F (163°C). Mix graham cracker crumbs, sugar, and melted butter. Press into a greased springform pan and bake for 10 minutes. Let cool.
Make the Cheesecake Filling: Beat cream cheese and sugar until smooth. Mix in eggs one at a time, then add vanilla, sour cream, and flour. Pour over the cooled crust.
Bake the Cheesecake: Wrap the pan’s bottom in foil and place it in a larger pan with hot water. Bake at 325°F for 50-55 minutes until the center jiggles slightly. Turn off the oven, crack the door, and let it cool for an hour. Refrigerate for at least 4 hours.
Make the Peach Topping: Cook peaches, brown sugar, cinnamon, and nutmeg over medium heat for 5 minutes. Stir in cornstarch slurry and cook until thickened. Let cool.
Make the Crumble Topping: Mix flour, sugars, cinnamon, and melted butter until crumbly. Bake at 350°F for 10-12 minutes until golden. Let cool.
Assemble: Spoon the peach topping over the chilled cheesecake, then sprinkle with the crumble.