Preheat your oven to 400°F (200°C). Cut the acorn squash in half from stem to tip and scoop out the seeds. Brush the flesh with olive oil and sprinkle with a little salt and pepper. Place the squash cut-side down on a parchment-lined baking sheet and roast for 25–30 minutes until the flesh is tender when pierced with a fork.
While the squash is roasting, heat a large skillet over medium-high heat. Add the ground sausage and cook, breaking it into crumbles, until browned and cooked through. Remove the sausage with a slotted spoon and set aside. In the same pan, add the onion and celery, sautéing for about 5 minutes until softened. Stir in the minced garlic and cook for another minute until fragrant.
In a large mixing bowl, combine the cooked sausage, sautéed vegetables, dried cranberries, chopped pecans, breadcrumbs, height, parsley, and sage. Toss everything together until well combined. If the mixture seems too dry, you can add a tablespoon of chicken broth or melted butter to help it bind.
Turn the roasted squash halves over so the flesh side is facing up. Divide the sausage mixture evenly among the four squash halves, mounding it up in the center. If using, sprinkle the Parmesan cheese over the top. Return the squash to the oven and bake for an additional 15–20 minutes until the filling is heated through and the top is golden brown.