Melt butter in a large skillet or saucepan over medium heat. Add garlic and cook, stirring frequently, until fragrant, about 1 minute.
Stir in chicken broth, milk, and penne. Bring to a boil and cook on high, stirring occasionally, until pasta is tender, about 10 to 12 minutes.
Add heavy cream, Parmesan cheese, and cooked chicken to the skillet and continue to cook for approximately 2 minutes.
Season with salt and pepper to taste. If the sauce is too thick, add more milk as needed until desired consistency is reached.
Garnish with parsley and serve immediately.