Start by roasting ½ of the peaches that are going to be in the filling of the cheesecake, the other half is going to be for the topping. Preheat the oven to 200c (400f) and prepare a baking sheet with parchment paper.
Slice the peaches into thick slices. Mix the peaches with cinnamon, nutmeg, and sugar until they are coated throughout.
Layer them onto the parchment paper-lined baking sheet into an even layer and bake in a 200c (400f) preheated oven for 10-15 minutes or until the peaches are softened slightly. Set aside to cool.
Lower the oven to 180c (350f) and prepare a 10-inch springform pan with parchment paper. Pulse graham crackers in a food processor until fine crumbs form. If you don’t have a food processor on hand, place the crackers in a Ziplock bag and smash the crackers with a cup until fine crumbs form. Into a small to medium mixing bowl, add the graham crackers crumbs, granulated sugar, cinnamon, and melted butter. Mix with a spoon until the crumbs are coated with butter. Transfer the crumbs into a prepared 10-inch springform pan, pressing evenly and firmly into the pan. Bake the crust in a 180c (350f) preheated oven for 8-9 minutes. Keep an eye on the crust and make sure it doesn’t burn. Take the crust out of the oven and let it cool to room temperature.
Meanwhile, make the streusel. In a medium mixing bowl, add the flour, oats, brown sugar, kosher salt, cinnamon, and mix until well combined. Add the melted butter and mix with a spoon until well combined.
Transfer the streusel onto a baking sheet lined with parchment paper and bake in a preheated 180c (350f) oven for 12-15 minutes.
Lower the temperature to 140c (280f). In a large mixing bowl, add the room-temperature cream cheese, sour cream, granulated sugar, and vanilla extract, and mix with an electric hand mixer until is creamy. Whisk the eggs in a small bowl add them to the cheesecake mixture and mix until the mixture is smooth. Sift the cornstarch into the mixture and mix until combined and there are no lumps of cornstarch showing. Pour ½ of the cheesecake mixture onto the crust and gently top it with ½ of the roasted peaches and ½ of the streusel.
Top with the other half of the cheesecake mixture. Bake it in a 140c (280f) preheated oven for about an hour or until the edges of the cheesecake are set, but the middle is a bit jiggly.
Open the oven door halfway, and let the cheesecake cool to room temperature for 1-2 hours.
After the cheesecake is cooled, wrap the cheesecake with plastic wrap tightly, and place the cheesecake in the fridge to cool completely for at least 5 hours.
Roast the remaining peaches for the topping. Carefully release the cheesecake from the pan and top it with the roasted peaches and the other half of the streusel.