Cut the spaghetti squash in half lengthwise and scoop out the seeds. Drizzle the inside with olive oil, and season with salt and pepper.
Place the squash cut-side down on a baking sheet and roast in the preheated oven for about 30-40 minutes, or until the flesh is tender and easily pulled into strands with a fork.
While the squash is roasting, heat a medium saucepan over medium heat. Add the minced garlic and sauté until fragrant (about 1 minute).
Pour in the heavy cream, stirring, and bring it to a simmer. Add the nutmeg and season with salt and pepper.
Reduce the heat and stir in the Gruyère and half of the Parmesan cheese until melted and well combined.
Once the squash is cooked, allow it to cool slightly before scraping the flesh with a fork to create spaghetti-like strands.
Combine the spaghetti squash strands with the creamy cheese mixture in a large mixing bowl, ensuring everything is well mixed.
Transfer the mixture into a greased baking dish. Top evenly with breadcrumbs and the remaining Parmesan cheese.
Bake in the oven for 20-25 minutes, or until the top is golden and bubbling.
Remove from the oven and let it cool slightly. Garnish with chopped fresh parsley before serving.