Preheat the oven to 400°F (200°C).
Brush the acorn squash halves with olive oil and season with salt and pepper.
Place the squash cut-side down on a baking sheet and roast for 25 to 30 minutes until tender.
Heat a skillet over medium heat and cook the Italian sausage until browned.
Add diced onion, celery, and minced garlic to the skillet; sauté for 3 to 4 minutes until softened.
Stir in dried thyme, sage, paprika, cooked rice or quinoa, Parmesan cheese, salt, and pepper to the filling mixture.
Flip the roasted squash halves cut-side up and fill each with the sausage mixture.
Top the filled squash with shredded mozzarella cheese.
Bake for an additional 10 to 12 minutes until the cheese melts and is bubbly.
Garnish with parsley or chili flakes and serve warm.