Preheat oven to 425°F.
Spray the cut sides of squash with oil and sprinkle with salt. Place squash face down on a large baking sheet. Bake at 425°F until tender and browned on the edges, 20 to 25 minutes.
Meanwhile, in a large sauté pan heat olive oil, then add onion and celery. Cook until celery is soft, 8 to 10 minutes.
Add sausage and cook until slightly browned.
Add mushrooms, garlic, thyme, and more salt and pepper (if needed) to the pan. Cook, stirring after 5 minutes, then cook covered for 2 minutes, or until the mushrooms are soft and cooked through. Divide (½ cup) between the squash halves. Garnish with parsley.
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