Melt butter in a large skillet over medium heat. Add the garlic and cook for 1-2 minutes or until fragrant. Add the chicken broth and spaghetti. Raise heat to high and bring to a boil. Reduce heat slightly and simmer until most of the liquid has evaporated, about 8-10 minutes. Add the milk or cream and grated Parmesan and cook, stirring, until the cheese has melted, the sauce thickened, and the pasta cooked to your liking, another 1-2 minutes.
Serve with freshly grated Parmesan, freshly ground black pepper, and parsley.