Prepare the Pan — Preheat the oven to 350°F (175°C). Line a 9×9-inch baking pan with parchment paper, leaving some overhang on the sides for easy removal.
Make the Graham Cracker Crust — Combine the graham cracker crumbs, melted butter, brown sugar, and cinnamon in a bowl. Stir until the crumbs are evenly moistened. Press the mixture firmly and evenly into the bottom of the prepared pan. Bake for 8 minutes, then remove from the oven and allow the crust to cool slightly.
Prepare the Peaches — Reduce the oven temperature to 325°F (165°C). Add the diced peaches, brown sugar, lemon juice, cornstarch, cinnamon, and nutmeg to a medium saucepan. Cook over medium heat for 5–7 minutes, stirring gently, until the peaches begin to soften and the juices thicken slightly. Remove from the heat and stir in the vanilla. Set aside to cool while preparing the cheesecake filling.
Make the Cheesecake Filling — Place the softened cream cheese and granulated sugar in a large bowl. Beat on medium-low speed until smooth and creamy. Add the eggs one at a time, mixing on low speed just until each egg is incorporated. Add the sour cream, vanilla, and flour. Mix just until smooth. Avoid overmixing once the eggs have been added.
Make the Cobbler Crumble — Combine the flour, brown sugar, cinnamon, and salt in a small bowl. Pour in the melted butter and stir with a fork until large, irregular crumbs form.
Assemble the Bars — Pour the cheesecake filling over the baked crust and spread it evenly. Spoon the peach mixture over the cheesecake. Gently swirl a few spoonfuls of the peach juices into the surface without mixing the layers completely. Scatter the cobbler crumble evenly over the peaches.
Bake — Bake at 325°F (165°C) for 40–47 minutes, or until the edges are set and the center still has a slight wobble when the pan is gently moved. Do not bake until the center is completely firm. It will continue to set as it cools.
Cool and Chill — Place the pan on a wire rack and let the cheesecake bars cool completely at room temperature. Cover and refrigerate for at least 4 hours, preferably overnight. Chilling completely is essential for clean slices and the proper cheesecake texture.
Slice and Serve — Lift the chilled cheesecake from the pan using the parchment paper. Cut into 16 bars with a sharp knife, wiping the blade clean between cuts. For the more rustic look shown in the photo, add a small spoonful of the reserved peach topping and a few loose crumble pieces before serving.