Place a large pot over medium-high.
Add in the chicken, without overcrowding the pot, if needed cook it in batches. Season with half of the salt and pepper, and cook it until nicely browned and cooked through, remove it from the pot and set it aside on a plate.
Add in the onion, garlic and broccoli. Cover and cook for 2-3 minutes. Season the veggies with the remaining salt, pepper, and dried basil. Cook and stir until the onions begin to become translucent.
Pour in milk and cream, and bring to a boil, stirring periodically.
Add pasta and cook it for 10-15 minutes, stirring frequently until it reaches your desired doneness.
Add in the ricotta and stir to melt.
Add Parmesan and mozzarella. Stir in chicken until well incorporated.
.If desired, preheat the oven to 400 degrees F, sprinkle the cheese after you stirred in the chicken and bake for 10 minutes, or until melted and bubbly.
Garnish with parsley and serve.