Put the chopped Gala apples, light brown sugar, 1 tablespoon butter, 1/2 teaspoon vanilla, and 1/2 teaspoon cinnamon in a medium pot over low heat and cook for 5 to 7 minutes, stirring occasionally, until the apples are softened but not browned or jammy.

Set the apple filling aside to cool completely before layering it into the batter.

Preheat the oven to 350°F and spray an 11-by-7-inch baking dish with baking spray.

In a large bowl, cream together the softened butter, dark brown sugar, and granulated sugar until the mixture looks lighter and fluffy.

Beat in the eggs one at a time, mixing after each addition, then add the kosher salt and 1 1/2 teaspoons vanilla extract.

In a separate medium bowl, whisk together the flour, baking powder, cinnamon, and pumpkin pie spice.

Gradually mix the dry ingredients into the wet mixture just until no dry flour streaks remain.

Spread half the thick batter into the prepared baking dish, spoon the cooled apple filling evenly over it, then dollop and gently spread the remaining batter on top.

Bake for 25 to 30 minutes, starting to check around 25 minutes, until a toothpick inserted into the bars comes out clean.

While the brownies bake, melt the 2 tablespoons butter with the maple syrup, 1/4 teaspoon vanilla, and pumpkin pie spice in a small pot over medium heat, then remove from the heat and whisk in the powdered sugar until smooth.

Spread the maple glaze evenly over the baked bars, then let everything cool completely before slicing into neat squares.