In a mixing bowl, whisk together heat-treated all-purpose flour, light brown sugar, ground cinnamon, and a pinch of salt until well combined. Cut in the cold, cubed unsalted butter until the texture resembles coarse crumbs. Set aside.

In a large bowl, gently toss the thick slices of slightly underripe peaches with melted butter, additional light brown sugar, and a sprinkle of cinnamon until all slices are coated. Set aside.

In a separate bowl, combine crushed graham crackers, granulated sugar, cinnamon, and a tiny pinch of salt. Stir in melted butter and press firmly into the bottom of a springform pan. Bake at 350°F for 8-10 minutes until lightly golden.

In a large mixing bowl, beat room-temperature cream cheese until smooth. Gradually add granulated sugar and cornstarch, mixing until well combined. Add eggs one at a time, mixing gently, then stir in vanilla and sour cream until creamy.

Pour half of the cheesecake batter over the baked graham cracker crust. Spoon the peach mixture over the batter, then top with the remaining cheesecake batter, smoothing the surface.

Preheat oven to 325°F and bake for approximately 1 hour and 15 minutes, until edges are set but the center has a slight jiggle. Turn off the oven and let cool inside for an hour.

After cooling, transfer the cheesecake to room temperature, cover with plastic wrap, and refrigerate for at least 4 hours, preferably overnight.