Preheat oven to 350 degrees. Line an 8"x8" pan with parchment paper. Set aside.
Melt 1 tablespoon butter in a medium skillet over medium heat. Add 2 tablespoons brown sugar and apple pieces. Stir to combine. Reduce heat to low and simmer for 5 minutes or until apples begin to soften. Remove from heat and let cool slightly.
In a medium bowl, melt remaining ½ cup butter. Stir in remaining 1 cup brown sugar.
Whisk in egg and vanilla extract.
Working in batches, stir in flour and salt. Mix until just combined. Fold in butterscotch chips and cooled apples. Pour into prepared baking dish.
Bake in preheated oven for 30 to 40 minutes or until bars are set. Let cool completely before cutting.
