Add the Mafaldine and stir well. Cover, reduce the heat to a gentle simmer and cook until the pasta is tender, about 10 minutes, stirring occasionally. Cooking time will vary by pasta brand and shape, so use tenderness as your endpoint.
Dice the rested chicken and add it back to the soup along with any juices that accumulated on the plate.
Reduce the heat to low. Add the Parmesan and Monterey Jack and stir until completely melted and incorporated into the creamy broth. Taste and adjust the seasoning as needed, remembering that the bacon will add additional salt when served.
Ladle into bowls and top generously with the crispy bacon, fresh parsley, and additional freshly grated Parmesan. Serve with warm buttery breadsticks, if desired.