Preheat the oven to 350°F. Grease a 9- by 13-inch baking pan with butter.

Add the butter to a medium saucepan over low heat, stirring occasionally. Check it after about 10 minutes; it should be a medium-brown color, not too light, not burned. Once it reaches that color, take it off the heat and let it cool.

Set aside about 1/4 cup of the browned butter. In a bowl of a mixer fitted with the paddle attachment, beat the remaining cooled brown butter and brown sugar until creamy.

Add the eggs and vanilla and mix, scraping the sides of the bowl, until fully incorporated. Add the flour, baking powder, salt, and pumpkin pie spice and mix until combined.

In the same saucepan, cook all but about 15 of the apple slices with reserved 1/4 cup of brown butter over medium-low heat until softened.

Press half the dough evenly into the prepared pan. Spread the cooked apples over the mixture. Press the remaining dough over the apples. Press the set aside slices into the top of the dough decoratively.

Bake the blondies for 45 minutes - 1 hour, or until a toothpick inserted into the center comes out with only a few crumbs stuck to it.

Let cool, then slice and serve. Store in the freezer or at room temperature.