Preheat the oven to 350 degrees F (175 degrees C).
Place squash, cut-sides down, on a rimmed baking sheet and add water to surround squash.
Bake in the preheated oven until tender, about 60 minutes.
Gently scrape squash strands into the center of each half using a fork.
Melt butter in a small saucepan over medium-low heat. Add garlic to hot butter and cook 1 to 2 minutes. Whisk in flour and cook for another minute while stirring until no lumps remain, 1 to 2 minutes more. Add cream cheese and stir until smooth, about 1 more minute. Stir in Parmesan cheese, salt, and pepper.
Spoon hot sauce equally on to each squash half. Gently pull up the squash strands to coat as much as possible with sauce. Top with extra Parmesan cheese if desired.
Set an oven rack about 6 inches from the heat source and preheat the oven's broiler. Place squash halves under the broiler until golden and bubbly, 2 to 3 minutes.
