Preheat the oven to 350°F (175°C). Line a 9″ x 13″ pan with aluminum foil and lightly spray with cooking spray.
In a bowl, combine the flour, baking powder, and salt. Mix well and set aside.
In the bowl of a stand mixer with a paddle attachment, beat the butter on high speed for 1 minute. Add the sugars and continue to beat for an additional 2 minutes, until the mixture is light and fluffy. Scrape down the sides as needed. Add the eggs and vanilla extract, and blend until well incorporated.
Gradually beat in the dry ingredients on low speed until just combined. Fold in the white chocolate chips.
Spoon half of the dough into the prepared pan, pressing it evenly across the bottom in a thin layer. Spread the cooled apple filling over the dough, gently pressing it into the dough. Sprinkle with half of the cinnamon/sugar mixture that was set aside.
Top with the remaining dough (I used a small ice cream scoop to place the dough evenly, then pressed it together to cover the apples. It's okay if some apples peek through—this looks great!). Sprinkle the remaining cinnamon/sugar mixture on top.
Bake for about 25 minutes, or until lightly golden and slightly puffed.
Allow the bars to cool before cutting. For the best results, store them in the refrigerator for up to 1 week.