Preheat the oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Brush the squash halves with 1 tablespoon olive oil and season with salt and pepper. Place cut-side down on the baking sheet and roast for 35–45 minutes, until fork-tender.
Meanwhile, heat the remaining olive oil in a large skillet. Add the carrots, shallots, and celery and cook for 5 to 6 minutes until softened.
Add the garlic and mushrooms and cook for 7 to 8 minutes, until the mushrooms release their moisture and begin to brown.
Pour in the white wine or vegetable broth. Stir in the cinnamon, thyme, sage, salt, and pepper, then cook for 2 to 3 minutes.
Fold in the cooked brown rice and fresh parsley. Cook for another 2 minutes and adjust the seasoning to taste.
Turn the roasted squash cut-side up and spoon the mushroom rice filling generously into each cavity.
Return the stuffed squash to the oven and bake for 10 minutes to warm the filling and lightly crisp the top.
Garnish with fresh parsley and toasted pumpkin seeds or pecans before serving.