Preheat oven to 425°. In a large ovenproof skillet (or in a large baking dish), toss butternut squash with olive oil, garlic and thyme. Season with salt and pepper, then scatter bacon on top.
Bake until the squash is tender and the bacon is cooked through, 20 to 25 minutes.
Remove skillet from oven and top with mozzarella and Parmesan. Bake for another 5 to 10 minutes, or until the cheese is melty.
Garnish with parsley and serve warm.