Heat oil in 5-quart Dutch oven over medium-high. Season chicken with salt and pepper; cook 4 minutes, stirring occasionally. It finishes with pasta.
Stir garlic 30 seconds; add broth, scrape bottom, and boil.
Add penne; steadily simmer uncovered 9 minutes, stirring bottom every 2 minutes. Add reserved water if pot dries.
Add milk, cream, and nutmeg; gently simmer 3 to 5 minutes until penne tender, chicken 165°F, and sauce flows between pieces.
Remove from heat; stir in Parmesan in 3 additions. Rest 2 minutes; loosen with remaining measured water if needed. Divide among 4 bowls.