Preheat the oven to 350 degrees and line a baking sheet with parchment paper.
Stir together the flour, baking powder, and apple pie spice in a bowl.
In a second bowl, beat the butter and brown sugar until light. Add the egg and vanilla extract and mix until smooth.
Fold the dry ingredients into the wet mixture until just combined, then stir in the diced apple.
Scoop the dough into eight portions and roll each in powdered sugar to coat fully.
Place the coated balls on the baking sheet and bake for 10 to 12 minutes until the edges set.
Remove from the oven and let the cookies cool on the sheet for five minutes before transferring to a rack.
Drizzle the cooled cookies with caramel sauce.