Place squash halves, cut side down, on 1 or 2 deep baking sheets filled with an inch of water. Place in oven and bake for 30 minutes. When done, remove from oven, remove the water, and flip the squash so it is cut side-up.
In a medium pot, sauté onions, carrots, and celery in ¼ cup water or vegetable broth until slightly browned, approximately 5 minutes. Add wild rice, brown rice, mushrooms, poultry seasoning, sage, black pepper, and remaining water or vegetable broth. Bring to a boil on medium-high heat and then simmer on medium-low heat for 30-40 minutes or until all liquid is absorbed. Add walnuts and parsley and cook for 2 more minutes. Remove from heat.
Spoon rice mixture into each squash. Cover in foil and return to oven. Bake for 20-25 additional minutes, or until squash is tender. Serve warm.