Preheat your oven to 400°F (200°C). Line a baking sheet with aluminum foil or parchment paper for easier cleanup.
Prepare the acorn squash by cutting each one in half lengthwise and scooping out the seeds. Brush the cut sides and cavity with 1 tablespoon of olive oil, then sprinkle with salt and pepper.
Place the squash halves cut-side down on the prepared baking sheet. Roast for about 30 minutes until they're just tender when pierced with a fork. They'll continue cooking later, so don't let them get too soft.
While the squash roasts, prepare the filling. Heat the remaining tablespoon of olive oil in a large skillet over medium heat. Add the Italian sausage, breaking it into crumbles as it cooks, until browned and no longer pink, about 5-7 minutes.
Add the diced onion and celery to the skillet. Cook until softened, about 3-4 minutes.
Stir in the diced apple, garlic, sage, and thyme. Cook for another 2 minutes until the apple begins to soften slightly and the garlic is fragrant.
Add the dried cranberries, chopped nuts, and spinach to the skillet. Cook until the spinach wilts, about 1-2 minutes.
Remove the skillet from heat and stir in the breadcrumbs, ¼ cup of the Parmesan cheese, and chicken broth. The mixture should be moist but not soggy. Season with salt and pepper to taste.
When the squash is ready, flip them over so the cut side is facing up. Brush the inside of each squash half with maple syrup.
Divide the sausage filling evenly among the four squash halves, mounding it slightly.
Sprinkle the remaining Parmesan cheese over the top of each stuffed squash.
Return to the oven and bake for an additional 15-20 minutes, until the filling is heated through and the tops are golden brown.
Garnish with fresh parsley before serving.