Cut the squash in half and scoop out. Brush each half of the acorn squash with olive oil. Place them face-side down onto a baking sheet and bake at 400F for 30 minutes.
Sauté the onions and celery for about 5 minutes. Add cranberries, hazelnuts, and spices, and sauté for another 5 minutes. Stir in the rehydrated mushrooms, water, cooked rice, salt, and pepper.
Evenly divide the filling between the 4 squashes, packing it down as you fill. Return to oven and bake for an additional 10-15 minutes, until squash is tender and fragrant.