Preheat the oven to 400 degrees F (200 degrees C).

Dot cut sides and cavity of squash halves with butter. Sprinkle with allspice, salt, and pepper. Place squash in a large roasting pan, cut-sides up.

Bake in the preheated oven until squash is fork tender, yet still holds its shape, 30 to 40 minutes. Remove from the oven and lower heat to 350 degrees F (175 degrees C).

Meanwhile, fry pork sausage in a large skillet over medium-high heat until browned and crumbly, 5 to 7 minutes. Remove sausage to a paper towel-lined plate. Drain and discard all but 2 teaspoons of fat from the skillet. Add onion to the skillet, and saute until brown, about 4 minutes. Stir in apples, mushrooms, and carrot; saute until carrots are cooked but still firm, 5 to 7 minutes.

Add sausage and water to the skillet and bring to a boil. Stir in stuffing mix, cover, and remove from the heat. Allow to sit, undisturbed, for 5 minutes. Uncover and season with sage, salt, and pepper. Stir in egg and parsley. Distribute stuffing mixture amongst 4 squash halves, mounding up stuffing if necessary.

Cover and bake in the 350 degrees F (175 degrees C) oven until egg is set, about 20 minutes. Uncover, and bake for another 10 minutes.