One Pot Garlic Parmesan Pasta aka the Lazy Cooks Fettuccine Alfredo

Name: One-Pot Garlic Parmesan Pasta (a.k.a. the Lazy Cook's Fettuccine Alfredo)
Ingredients: 1 tablespoon olive oil; 4 cloves garlic, minced; 2 cups vegetable broth (or chicken stock); 1 cup milk (more as needed); 2 tablespoons unsalted butter; 8 ounces fettuccine or other long noodle; Salt and pepper, to taste; 1/4 cup freshly grated Parmesan; Chopped parsley, for garnishing