Preheat oven to 400°F (200°C).
In a large bowl, toss butternut squash with olive oil, salt, pepper, garlic, and thyme.
Spread the squash mixture in a greased casserole dish and roast for 25 minutes until tender.
Remove from oven and stir in cream and mozzarella cheese.
Top with Parmesan and return to the oven for 10 minutes or until bubbly and golden.
Sprinkle with chopped parsley before serving, if desired.