Place squash cut side down in a glass dish. Cook in microwave for 20 minutes on HIGH, until almost tender.
In a saucepan over medium heat, melt butter and add celery and onion; saute until transparent. Stir in mushrooms; cook 2 to 3 minutes more. Sprinkle with salt, pepper, and parsley. Divide mixture in half, spoon into the squash and cover.
Cook 15 minutes in the preheated 350 degrees F (175 degrees C) oven. Uncover, sprinkle with cheese and put back in the oven until the cheese bubbles.