Make the crust: Mix graham cracker crumbs, melted butter, brown sugar, and cinnamon. Press firmly into a springform pan, then bake at 175°C / 350°F for 8–10 minutes. Let cool slightly.
Prepare the filling: Beat softened cream cheese until smooth. Add sugar gradually, then mix in eggs one at a time. Add sour cream, vanilla, and cornstarch. Mix just until combined.
Prepare the peaches: Slice peaches evenly, then toss with brown sugar, cinnamon, lemon juice, butter, and optional nutmeg. For a softer, syrupy topping, cook for 5–7 minutes, then cool slightly.
Assemble: Pour cheesecake filling into the cooled crust. Spoon peaches evenly over the top, then add crumble topping if using. Tap the pan gently to remove air bubbles.
Bake: Bake at 160–170°C / 325°F for 55–75 minutes, until the edges are set and the center slightly jiggles. Turn off the oven, crack the door, and let it cool slowly.
Chill: Refrigerate for at least 4–8 hours, preferably overnight, before slicing. This helps the cheesecake firm up and improves the flavor.
