Preheat the oven to 400ºF and adjust the rack to the middle position. Place the 4 squash halves, cut-side down on a baking sheet lined with parchment paper. Bake for 45 minutes. You can do this earlier in the day if needed.
Melt the butter over medium heat in a saucepan. Stir in the chopped and granulated garlic, and arrowroot. Whisking constantly, add in the milk and cream, and continue to cook until just starting to thicken, about 5-7 minutes. Whisk in the parmesan and salt. Stir in the shredded chicken.
Using a potholder, carefully pick up a spaghetti squash half and, using a fork, scrape the spaghetti squash out of the skin and into a large bowl. Repeat with remaining 3 squash halves. Pour Alfredo sauce over the squash and stir until incorporated. Spoon an even amount of squash mixture back into each of the 4 squash “bowls”. Top with mozzarella cheese. Bake for 30 minutes until mozzarella cheese is turning golden brown and bubbly.