Preheat your oven to 325°F (163°C).

In a mixing bowl, combine graham cracker crumbs, sugar, and melted butter to form a sandy mixture. Press this mixture into the bottom of a 9-inch springform pan and bake for about 10 minutes.

In a saucepan, combine chopped peaches, brown sugar, cinnamon, lemon juice, and cornstarch over medium heat. Cook for 5-8 minutes until thickened.

In a bowl, beat cream cheese and sugar until smooth, then add eggs, one at a time, followed by vanilla and sour cream.

Pour cheesecake filling over the cooled crust, then spoon the peach mixture on top.

In a bowl, mix flour, sugars, cinnamon, and cold butter until crumbly. Sprinkle on top of the peach layer.

Place the springform pan in a baking dish filled with hot water and bake for 60-70 minutes.

After baking, let the cheesecake cool for about 1 hour, then refrigerate for at least 6 hours or overnight.

Run a knife around the edge before removing the sides. Serve with whipped cream or vanilla ice cream if desired.