Preheat the oven to 325°F (165°C).

Lightly grease a 9×13-inch (23 × 33 cm) baking pan. Line the pan with parchment paper, leaving enough overhang on the long sides to lift the cheesecake from the pan after it has chilled.

Add the diced peaches, brown sugar, lemon juice, cinnamon, and nutmeg to a medium saucepan.

Cook over medium heat for about 8 to 10 minutes, stirring gently and frequently, until the peaches begin to release their juices and the liquid becomes lightly thickened.

While the peaches cook, dissolve the cornstarch in the water.

Pour the cornstarch mixture into the pan and stir immediately. Continue stirring for about 1 minute, or until the mixture thickens.

Transfer the peach filling to a shallow bowl and cover with plastic wrap placed directly on the surface. Let it cool completely before assembling the cheesecake.

In a medium bowl, stir together the graham cracker crumbs and brown sugar.

Add the melted butter and mix until all the crumbs are evenly moistened.

Transfer the mixture to the prepared pan. Press it firmly and evenly into the bottom of the pan using the bottom of a measuring cup or glass.

Bake the crust for 12 minutes. Remove it from the oven and set it aside to cool slightly.

In a medium bowl, whisk together the flour, brown sugar, cinnamon, nutmeg, and salt.

Add the softened butter. Use a fork, pastry cutter, or your fingertips to work the butter into the dry ingredients until large, moist crumbs form.

Place the crumble in the refrigerator while you prepare the cheesecake batter.

Using a hand mixer or stand mixer fitted with the paddle attachment, beat the cream cheese on medium-low speed until completely smooth and creamy, about 2 minutes.

Add the brown sugar and granulated sugar. Mix on low to medium-low speed until smooth.

Add the sour cream and mix until combined.

Add the eggs one at a time, mixing on low speed after each addition just until incorporated. Add the vanilla extract and salt with the final egg.

Pour the cheesecake batter over the baked crust and spread it into an even layer.

Gently spoon the cooled peach filling evenly over the cheesecake batter.

Remove the crumble from the refrigerator and sprinkle it evenly over the peach layer.

Bake at 325°F (165°C) for 60 to 75 minutes.

Remove the pan from the oven and place it on a wire rack. Let the cheesecake cool completely at room temperature.

Cover the pan and refrigerate the cheesecake for at least 6 hours, preferably overnight, before lifting it from the pan and slicing.

In a small bowl, whisk the cream cheese and butter until smooth.

Add the powdered sugar and mix until combined.

Add the milk, 1 tablespoon at a time, until the glaze reaches a smooth, pourable consistency.

Use the parchment paper overhang to carefully lift the chilled cheesecake from the pan. Transfer it to a cutting board.

For clean slices, use a large, sharp knife and wipe the blade clean between cuts.

Drizzle the cream cheese glaze over the entire cheesecake before slicing, or drizzle it over each individual bar just before serving.