Preheat oven to 375 F. Line a baking dish with foil. Cut spaghetti squash in half lengthwise, season the inside with 1 tbsp olive oil each, salt and pepper to taste. Place the boats cut side down and roast for 45-50 minutes. Let it cool for 5 minutes and carefulli using a fork shred to get the noodles.
In the mean time prepare the Alfredo sauce. Melt butter in a pan over medium heat. Add garlic, salt, pepper, corn starch, (nutmeg, optional) and stir. Add the heavy cream. Bring to a boil, cook for 1 minute and reduce the heat to low. Add the Parmesan. Cook until the sauce thickens. Add the chicken, cook for 1 minute.
Turn the oven to broil at 400 F.
Divide the sauce between both spaghetti squash boats. Top with mozzarella cheese. Broil for 2-3 minutes, keeping an eye on the dish, until the cheese is melted. Serve immediately.