Preheat the oven to 400ºF / 200ºC degrees and lay the halved squash skin side down onto two baking sheets.
Drizzle with olive oil and season with salt and pepper then roast in the oven for around 40 minutes until tender. Remove from the oven and allow to cool just a little so easier to handle.
Whilst the squash is roasting, in a large skillet melt the butter over a medium heat then add in the flour and cook for a minute stirring continuously.
Add in the milk and broth whilst stirring and bring to a simmer.
Add in the cream and parmesan and season with salt and pepper.
Cook stirring regularly for around ten minutes until the sauce has thickened. Add in the cooked chicken and allow to heat through.
Using a fork scrape the insides of the roasted squash into strands creating wells in the center of each half.
Add the shredded squash into the sauce and stir to combine.
Scoop equal portions of the chicken and Alfredo sauce into each squash half then evenly sprinkle the top of each one with the shredded mozzarella.
Bake in the oven for a further 15 minutes until the cheese is melted and bubbling.