Preheat oven to 350 degrees. Fill a large casserole dish with ½” water, set aside. Cut the squash in half length-wise. Scoop out seeds and place the squash cut side up in the casserole dish. Poke holes in the squash flesh with a fork. Season with salt and pepper. Add 4 Tbsp butter to each of the cavities. Cover with foil and bake for ½ hour. Set aside to cool.
Heat olive oil in a large skillet over medium heat. Cook the sausage, onions and celery, crumbling the sausage as it cooks. Add garlic and sauté a few minutes more.
Remove skin from squash and cut into cubes. Spread squash on a large baking sheet and drizzle lightly with olive oil to coat. Bake squash 15-20 minutes or until tender.
Transfer squash into a large mixing bowl. Add cubed stuffing, sausage mixture, beaten eggs, melted butter, salt, pepper and fresh sage. Slowly add in chicken broth until bread is completely moistened but not soggy.
Transfer to a greased 9×13 pan. Bake at 350 degrees for 30-45 minutes or until heated through. Sprinkle with fresh thyme before serving.