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.
Make the Peach Filling
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.
The peaches should soften slightly but still hold their shape. Do not cook them until they become mushy.
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. The peach filling should be thick enough to coat the back of a spoon.
If using frozen peaches, or if the mixture seems too runny or watery, add an additional ½ tsp cornstarch dissolved in 1 tsp water at a time until the desired consistency is reached.
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.
Make the Graham Cracker Crust
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.
Make the Crumble Topping
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.
Make 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, scraping down the sides and bottom of the bowl as needed.
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.
Assemble the Cheesecake
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. Be careful not to press it into the batter so the peaches don't sink.
Remove the crumble from the refrigerator and sprinkle it evenly over the peach layer. Break up any very large pieces as you scatter it, but leave a mixture of small and large crumbs for the best texture.
Bake
Bake at 325°F (165°C) for 60 to 75 minutes.
The bars are done when the edges are set and slightly puffed while the center still has a gentle wobble when the pan is lightly shaken. The center should not look liquid or slosh from side to side.
An instant-read thermometer inserted into the center of the cheesecake should register about 150°F to 155°F (66°C to 68°C). Avoid baking it beyond 160°F (71°C), as the cheesecake may become dry, grainy, or more likely to crack.
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.
Make the Cream Cheese Glaze
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.
If the glaze is too runny, add more powdered sugar. If it is too thick, add more milk by the teaspoon until it reaches the desired consistency.
Slice and Decorate
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.
Notes
Peaches: Use ripe but still firm peaches. Very soft or overripe peaches may break down too much during cooking and release excessive liquid.Fresh or Frozen Peaches: Fresh peaches will give the best texture. Frozen peaches may also be used, but they can release more water, so you may need additional cornstarch while cooking the filling.Room-Temperature Ingredients: The cream cheese, sour cream, and eggs should be at room temperature before mixing. Cold ingredients are more difficult to combine and may leave lumps in the cheesecake batter.Cream Cheese: Use full-fat, brick-style cream cheese. Cream cheese sold in tubs is softer and may prevent the cheesecake from setting properly.Sour Cream Substitute: The sour cream can be replaced with an equal amount of full-fat plain Greek yogurt. Regular plain yogurt may also be used, but choose a thick variety rather than a thin or watery yogurt.Crumble Texture: The butter should be soft enough to work into the flour but not melted. Melted butter will create a flatter, denser topping instead of distinct crumbs.Avoid Overmixing: After adding the eggs, mix the batter only until combined. Overmixing incorporates excess air, which can cause the cheesecake to rise, crack, or sink as it cools.Do not Overbake: The center should still wobble slightly when the cheesecake is removed from the oven. It will continue to set as it cools and chills.Chilling: Do not attempt to lift or slice the cheesecake while it is warm. It needs several hours in the refrigerator to become firm enough for clean bars.Parchment Paper: Leave a generous overhang on two opposite sides of the pan. This creates handles that make it easier to lift the chilled cheesecake out without damaging the crumble topping.Glaze Consistency: Use less milk for a thicker, more defined drizzle or more milk for a thinner glaze that can be poured over the entire cheesecake.Storage: Store the cheesecake bars in an airtight container in the refrigerator for up to 5 days.Freezing: Freeze the bars for up to 2 months. Wrap them well and thaw overnight in the refrigerator. Individual slices will thaw faster than the whole cheesecake. For quicker serving, let a frozen slice sit at room temperature for about 40 minutes, or until thawed and ready to serve.