In a bowl, combine graham cracker crumbs, sugar, and melted butter. Mix until well combined.
Press the mixture firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes, then remove from the oven and let cool.
Make the Cheesecake Filling:
In a large mixing bowl, beat the softened cream cheese and sugar until smooth. Add the vanilla extract and scraped seeds from the vanilla bean, mixing until combined.
Add the eggs one at a time, mixing well after each addition. Stir in the sour cream until fully combined.
Pour the cheesecake filling over the cooled crust in the springform pan.
Bake the Cheesecake:
Bake in the preheated oven for about 50-60 minutes, or until the edges are set and the center is slightly jiggly. Turn off the oven and let the cheesecake cool in the oven with the door slightly open for about 1 hour.
Once cooled, refrigerate for at least 4 hours or overnight.
Prepare the Peach Topping:
In a saucepan, combine sliced peaches, sugar, cinnamon, lemon juice, and cornstarch (if using). Cook over medium heat for about 5-7 minutes until the peaches soften and the mixture thickens slightly. Remove from heat and let cool.
Make the Salted Caramel Sauce:
In a saucepan over medium heat, melt the sugar, stirring constantly until it turns a golden color.
Carefully add the butter and stir until melted, then slowly add the heavy cream, stirring continuously until smooth. Remove from heat and stir in the sea salt. Let cool slightly.
Assemble the Cheesecake:
Once the cheesecake is set, remove it from the springform pan. Top with the peach mixture and drizzle with salted caramel sauce.
Serve:
Slice and enjoy your Vanilla Bean Cheesecake topped with Peach Cobbler and Salted Caramel!