Position the oven rack in the center and preheat the oven to 400 degrees F. Grease a standard 12 muffin pan or line it with paper cups.
Whisk/sift together the all purpose flour, whole wheat flour, baking soda, sea salt and pumpkin pie spice.
In a stand mixer with the paddle attachment (or using a hand mixer), cream the butter and sugars together on high speed until light and fluffy. Turn the speed down to low and add the eggs, one at a time, allowing each to incorporate completely for about 30 seconds.
By hand, stir in the the vanilla, acorn squash and buttermilk. Do not over-mix or the batter might break (the muffins will still be fine if it does, you'll just want to move more quickly).
Once the wet ingredients are combined, stir in the flour mixture by hand, followed by the chopped apples.
Use a muffin scoop to evenly distribute the batter into the prepared muffin pan. Bake for 20 minutes. Allow to cool before serving.
Notes
There are several ways to prepare pureed acorn squash. I sliced the acorn squash in half, scooped out the seeds, rubbed a bit of olive oil on the inside and then roasted it in the oven at 400 degrees F for a little over an hour. The length of time will depend on the size of the squash, test it with a fork. Once the squash is cooked, allow it to cool and then scoop out the flesh and puree it with a food processor or hand blender.To make your own pumpkin pie spice blend, combine the following (please note that this makes more than you need for the muffins):