Heat-treat the flour in the microwave for about 90 seconds. Allow it to cool completely.
Make the crumble by combining flour, brown sugar, cinnamon, salt, and cold butter until the mixture resembles wet sand. Refrigerate.
Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper.
Toss peaches with melted butter, brown sugar, and cinnamon.
Arrange peaches in a single layer on the baking sheet and roast for 15 minutes. Cool completely.
Reduce oven temperature to 350°F (175°C). Prepare a 9-inch springform pan with nonstick spray and parchment strips around the sides.
Mix graham cracker crumbs, sugar, cinnamon, salt, and melted butter.
Press firmly into the bottom and sides of the pan.
Bake crust for 10 minutes and cool.
Reduce oven temperature to 325°F (163°C).
Beat cream cheese, sugar, and cornstarch on low speed until smooth.
Add eggs one at a time, mixing gently after each addition.
Mix in vanilla and egg yolk.
Fold in sour cream until fully incorporated.
Pour half of the cheesecake batter into the crust.
Layer half of the roasted peaches over the batter.
Sprinkle about three-quarters of the crumble mixture on top.
Add the remaining batter and smooth the surface.
Place a roasting pan filled with hot water on the lower oven rack to create steam.
Bake the Peach Cobbler Cheesecake for 1 hour and 15 minutes.
Turn off the oven and leave the cheesecake inside with the door slightly open for 1 hour.
Cool at room temperature for 30 minutes.
Refrigerate for at least 4 hours, preferably overnight.
Top with remaining roasted peaches and crumble before serving.