Add butter and sliced peaches to a medium sized sauce pot and turn the heat to medium.
When the butter melts, add all of the remaining ingredients except cornstarch to the pot and allow to come to a boil.
In a small bowl, combine cornstarch and 1-2 tbsp of the liquid from the pot to create a slurrie. Add to the pot stir. Reduce heat and allow to simmer for about 10 minutes.
Set aside to cool completly.
Crust
Preheat the oven to 350°
In a food processor, pulse the graham crackers until no large pieces are left. You can also place them in a large bag and crush them with a rolling pin or small pot.
Pour the crushed graham crackers in a mixing bowl and add in sugar, melted butter and salt. Combine until all the crumbs are moist.
Pour the mixture into a 9 inch springform pan lined on the bottom with parchment paper and sprayed with cooking spray. Using a cup, press the crumbs into an even layer.
Bake for 10 minutes, remove from oven and all to cool.
Cheesecake Batter
In a stand mixer with a paddle attachment, whip cream cheese and sugar into fluffy.
On a low speed setting, add eggs in one at a time until each is completely combined.
Add in sour cream, lemon juice, flour and vanilla. Mix until all ingredients are incorporated
Cheesecake Assebmly
Reduce oven temperature to 300°
Pour half of the cheesecake batter into the springform pan over the crust.
Add half of the peach mixture over the batter (be careful to not add too much of the liquid/syrup)
Pour the remaining batter over the peaches, then top with the remaining peaches in the center, and sprinkle half of the crumble around the edges.
Place the springform pan inside of a larger rimmed baking sheet or shallow roasting pan. Fill the larger pan with about 1 inch of water to create a waterbath around the cheesecake. Place both pans in the oven.
Bake for 1 hour and 20 minutes until the middle is set (it will still be juggly).
Turn off the oven and leave the cheesecake in the oven for 1 hour. DO NOT open the oven door.
Move to the refrigerator and allow to cool for at least 4 hours, overnight is best.
Top with remaining crumble and serve as is or with bourbon caramel sauce