Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving enough overhang to lift the bars from the pan.
In a medium bowl, combine the flour, brown sugar, granulated sugar, cinnamon, salt, and baking powder. Stir in the melted butter and egg yolk until a crumbly mixture forms.
Press enough of the mixture firmly into the bottom of the prepared pan to form an even crust, reserving the remaining mixture for the topping.
Bake the crust for 10 minutes. Remove from the oven and set aside while you prepare the remaining layers.
Toss the diced apples with the brown sugar, cinnamon, and nutmeg. If the apples release excess liquid while they sit, leave the extra liquid behind when assembling the bars.
In a separate bowl, beat the softened cream cheese and granulated sugar until smooth and creamy. Mix in the sour cream and vanilla.
Add the egg and mix just until combined.
Spread the cheesecake filling evenly over the warm crust.
Spoon the spiced apples evenly over the cheesecake filling. Sprinkle the reserved crumble mixture over the apples.
Bake at 350°F for 40 to 45 minutes, or until the edges are set and the center still has a slight jiggle.
Cool to room temperature, then refrigerate for at least 4 hours or overnight before slicing.
To make the maple glaze, whisk together the powdered sugar, maple syrup, milk, vanilla, and salt until smooth. Add a small amount of additional milk if needed to reach a thick but drizzleable consistency.
Drizzle the maple glaze over the completely chilled bars. Allow the glaze to set slightly, then slice and serve.