1. Preheat oven to 325°F (165°C). Line the bottom of a 9-inch springform pan with parchment paper and lightly grease the sides.

2. In a bowl, combine graham cracker crumbs, granulated sugar, brown sugar, cinnamon, and salt. Stir in melted butter until the crumbs are evenly moistened.

3. Press the crumb mixture firmly into the bottom and slightly up the sides of the prepared pan. Bake for 8–10 minutes, then set aside to cool while you prepare the filling.

4. In a large mixing bowl, beat the softened cream cheese until completely smooth and free of lumps.

5. Add granulated sugar and continue beating until creamy and glossy, scraping down the bowl as needed.

6. Mix in sour cream, heavy cream, vanilla extract, lemon juice, and salt until just combined.

7. Sprinkle cornstarch over the mixture and blend on low speed until incorporated.

8. Add eggs one at a time, mixing on low just until combined and avoiding overbeating.

9. Pour the cheesecake batter over the cooled crust and smooth the top with an offset spatula.

10. Place the springform pan on a baking sheet. Bake for 45–55 minutes, or until the edges are set and the center still has a slight jiggle when gently shaken.

11. Turn off the oven, crack the door slightly, and let the cheesecake cool in the oven for 30 minutes.

12. Remove from the oven and cool to room temperature. Run a knife around the edge to loosen, then cover and refrigerate for at least 4 hours or overnight until fully chilled.

13. For the peach topping, add peaches, brown sugar, granulated sugar, butter, lemon juice, vanilla, cinnamon, nutmeg, and salt to a medium saucepan.

14. Cook over medium heat, stirring occasionally, until the peaches release their juices and the mixture begins to bubble.

15. In a small bowl, whisk cornstarch and water into a smooth slurry. Stir the slurry into the peach mixture.

16. Continue cooking for 2–3 minutes, until the sauce thickens and becomes glossy and the peaches are tender. Remove from heat and cool to just warm or room temperature.

17. Release the chilled cheesecake from the springform pan and transfer it to a serving plate.

18. Spoon the peach cobbler topping over the top of the cheesecake, letting some syrup drip down the sides.

19. Slice with a sharp knife dipped in warm water and wiped dry between cuts for clean slices.

20. Serve as-is or with whipped cream, and refrigerate any leftovers in an airtight container.