Preheat the oven to 325°F (165°C).
Line a 9 × 9-inch baking pan with parchment paper, leaving overhang on two sides.
Combine the graham cracker crumbs, melted butter, brown sugar, and cinnamon.
Press the mixture firmly into the bottom of the prepared pan.
Bake the crust for 8 minutes, then remove it from the oven and cool slightly.
Beat the softened cream cheese on medium-low speed until smooth.
Add the granulated sugar and mix just until combined.
Add the sour cream, vanilla extract, and salt and mix until smooth.
Add the egg and mix on low speed only until incorporated.
Spread the cheesecake mixture evenly over the crust.
In a separate bowl, combine the sliced apples, brown sugar, cinnamon, nutmeg, lemon juice, and cornstarch.
Arrange the seasoned apple slices naturally over the cheesecake layer.
Combine the flour, rolled oats, brown sugar, and cinnamon for the crumble.
Add the melted butter and mix with a fork until irregular crumbs form.
Scatter the crumble loosely over the apple layer.
Bake for 40–45 minutes, until the edges are set and the crumble is golden.
Cool completely at room temperature.
Cover and refrigerate for at least 4 hours, preferably overnight.
Lift the chilled bars from the pan using the parchment paper.
Cut into 16 bars with a sharp knife, wiping the blade between cuts.