Melt butter in a large skillet over medium high heat. Add garlic and cook, stirring frequently, until fragrant, about 1-2 minutes.
Stir in chicken broth, milk and fettuccine; season with salt and pepper, to taste.
Bring to a boil; reduce heat and simmer, stirring occasionally, until pasta is cooked through, about 18-20 minutes (adjust time if using another type of pasta).
Stir in Parmesan. If the mixture is too thick, add more milk as needed until desired consistency is reached.
Serve immediately, garnished with parsley, if desired.