Preheat oven to 350 degrees F (175 degrees C). Grease a baking sheet.
Place squash, cut-side up, on the prepared baking sheet. Place 1 tablespoon butter and 1 tablespoon brown sugar into the cavity of each squash half.
Bake in the preheated oven until skin is crispy and flesh is tender, about 1 hour. Cool until squash is easily handled, about 10 minutes.
Scoop flesh into a large bowl; add remaining butter, brown sugar, and apple pie spice. Whip squash mixture with an electric mixer on medium speed until fluffy.