Bring a large pot of water to a boil and season generously with salt. Cook fettuccine until al dente, reserving ½ cup of pasta water before draining.
In a large skillet over medium heat, melt the butter. Add the minced garlic and sauté for about 1-2 minutes, until fragrant.
Pour in the heavy cream, stirring continuously. Let it simmer gently for about 5 minutes—do not let it boil.
Lower the heat and gradually add the grated Parmesan cheese, stirring constantly until smooth and creamy.
Add the cooked fettuccine to the sauce, tossing to coat. If the sauce is too thick, add a splash of reserved pasta water.
Taste and season with salt and black pepper.
Serve immediately, garnished with fresh parsley and extra Parmesan if desired.