Preparation Steps

• Preheat oven to 325°F. Line the bottom of a 9-inch springform pan with parchment and lightly grease the sides. Wrap the outside of the pan with two layers of heavy-duty foil for a water bath.
• Make the crust: Stir graham crumbs, 0.25 cup sugar, and 0.5 teaspoon cinnamon. Mix in 0.5 cup melted butter until evenly moistened. Press firmly into the bottom and 1 inch up the sides of the pan. Bake 10 minutes, then cool while you make the filling.
• Heat a kettle of water for the water bath. Place the wrapped pan in a large roasting pan to prepare for baking.
• Make the filling: Beat cream cheese on medium speed until smooth and fluffy, 2 minutes. Add 1 cup sugar and beat 1 minute more. Mix in sour cream, 2 teaspoons vanilla, and 2 tablespoons cornstarch. Add eggs and yolk one at a time on low speed just until combined. Do not overmix.
• Pour the filling over the crust. Tap the pan gently to release air bubbles.
• Bake the cheesecake: Pour hot water into the roasting pan to reach halfway up the springform. Bake 55 to 60 minutes until edges are set and the center wobbles slightly.
• While cheesecake bakes, make the peach topping: In a skillet, combine peaches, 0.5 cup brown sugar, 0.25 cup sugar, lemon juice, 1 teaspoon cinnamon, 0.25 teaspoon nutmeg, and 1.5 tablespoons cornstarch. Cook over medium heat, stirring, until peaches are tender and the juices thicken, 6 to 8 minutes. Remove from heat to cool slightly.
• Make the crumble: In a bowl, mix flour, oats, 0.25 cup brown sugar, 0.5 teaspoon baking powder, and 0.25 teaspoon salt. Stir in 0.25 cup melted butter and 0.5 teaspoon vanilla until large clumps form. Spread on a parchment-lined sheet and bake alongside the cheesecake for 8 to 10 minutes until just golden. Cool slightly and crumble into chunks.
• When the cheesecake reaches the wobble stage, remove from oven. Leave the oven on. Carefully lift the springform from the water bath, remove the foil, and set the pan on a baking sheet.
• Spoon the peaches evenly over the cheesecake, leaving a small border at the edge. Sprinkle the crumble over the peaches.
• Return to the oven and bake 10 to 15 minutes more to set the topping. Turn off the oven, crack the door, and let the cheesecake rest inside 30 minutes.
• Cool completely on a rack, then refrigerate at least 4 hours or overnight. Run a knife around the edge and release the springform before slicing.
• Serve chilled. For clean slices, warm a sharp knife under hot water and wipe between cuts.