Preheat the Oven:
Preheat your oven to 325°F (165°C). Grease and line a 9-inch springform pan with parchment paper or non-stick spray.

Make the Crust:
In a medium bowl, combine the graham cracker crumbs, granulated sugar, and melted butter. Stir until the mixture resembles wet sand. Press the mixture into the bottom of the prepared pan to form an even crust. Bake for 8-10 minutes, until golden brown, then remove from the oven and allow to cool.

Make the Cheesecake Filling:
In a large bowl, beat the softened cream cheese and sugar until smooth and creamy. Add the vanilla extract and mix until combined. Add the eggs one at a time, beating well after each addition. Stir in the sour cream, heavy cream, and flour until smooth. Pour the cheesecake filling over the cooled crust, spreading it evenly.

Bake the Cheesecake:
Bake for 50-60 minutes, or until the center is set but still slightly jiggly. Turn off the oven and let the cheesecake cool in the oven with the door slightly ajar for 1 hour. Afterward, allow it to cool completely on a wire rack. Refrigerate for at least 4 hours, or overnight, for best results.

Make the Peach Topping:
In a saucepan, combine the sliced peaches, sugar, lemon juice, cinnamon, and nutmeg. Cook over medium heat for about 5-7 minutes, stirring occasionally, until the peaches begin to soften and release their juices. If you want a thicker topping, add the cornstarch mixture and cook for an additional 1-2 minutes until thickened. Remove from heat and allow it to cool.

Assemble the Cake:
Once the cheesecake has fully chilled, spoon the peach topping over the cheesecake, spreading it evenly. Garnish with fresh mint leaves and whipped cream if desired.

Serve:
Slice and serve your delicious Peach Cobbler Cheesecake, enjoying the perfect blend of creamy cheesecake and sweet, spiced peaches in every bite!