Preheat the oven to 400F.
Cut the squash in half and scoop out the seeds. Drizzle with olive oil, salt, and pepper. Place on a baking sheet, cut side down, and roast for 40 minutes.
While the squash is roasting, heat olive oil in a large skillet over medium heat. Add sausage and cook until browned, about 8 minutes. Remove from skillet.
Add mushrooms, onion, garlic, sage, thyme, salt, and pepper to the skillet. Sauté until the mushrooms are cooked and liquid is reduced, about 8-10 minutes.
Add sausage back to the skillet. Stuff squash with sausage filling and bake for 10 minutes.
Top with fresh thyme and grated parmesan cheese and serve.