Preheat oven to 425°F. Spray the cut sides of the squash with oil and sprinkle with salt. Place face down on a large baking sheet. Bake until tender and browned on the edges, about 20 to 25 minutes.

Meanwhile, in a large saute pan cook sausage on medium heat, breaking up the meat into small pieces as it cooks until browned. Add the onion and celery; cook until soft, about 8 to 10 minutes.

Add the mushrooms and thyme to the pan, season with salt and pepper if needed, and cook, stirring for 5 minutes. Cover and cook for 2 minutes until mushrooms are soft.

Divide the filling evenly among the squash halves. Top with parmesan cheese and bake for an additional 10 minutes.