Wash the squash under cool water, cut in half lengthwise, scoop out the seeds, drizzle with olive oil, and sprinkle with salt and black pepper.
Preheat oven to 400°F (200°C), place squash cut-side down on a baking sheet, and roast for 30-40 minutes until tender.
In a bowl, whisk together heavy cream, minced garlic, dried thyme, paprika, and cayenne pepper to make the cheese sauce.
Scrape the cooked squash into strands, combine with cheese sauce and shredded cheeses in a mixing bowl.
Transfer mixture to a greased 9x13-inch baking dish, sprinkle with Parmesan cheese, and bake for 25-30 minutes until golden and bubbly.