Place a rack in the center of your oven and preheat the oven to 350°F
Wash and dry the squash. Trim off the top and bottom ends, then carefully slice it in half lengthwise. Scoop out the seeds. Place it cut-side up on the prepared baking sheet.
Brush the cut sides of the squash with 1 tablespoon of the olive oil and the maple syrup. Sprinkle with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Bake for 1 hour 15 minutes, or longer depending upon the size of your squash, until very tender and the squash pierces easily with a fork.
Carefully scoop out the flesh and place it in the bowl of a stand mixer or a large mixing bowl. Add the nutmeg, milk, Parmesan, parsley, and remaining 1 tablespoon olive oil, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Mash the butternut squash on ow speed.