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. 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.