Heat oil in a 5-quart Dutch oven over medium-high heat. Season chicken with salt and pepper and cook for 4 minutes, stirring occasionally; it will finish cooking with the pasta.
Add garlic and stir for 30 seconds. Pour in broth, scrape the bottom and bring to a boil.
Stir in penne, reduce to a steady simmer and cook uncovered for 9 minutes, stirring from the bottom every 2 minutes. Add a little reserved water if the pot gets dry.
Stir in milk, cream and nutmeg. Simmer gently for 3 to 5 minutes until penne is tender, chicken reaches 165°F and the sauce remains loose enough to flow between the pieces.
Remove from the heat, stir in Parmesan in 3 additions and rest for 2 minutes. Loosen with any remaining measured water if necessary and divide among 4 bowls.