In a large saucepan over medium heat, melt the butter. After the butter has melted, add the minced garlic and simmer for a few minutes, or until it is aromatic.
As you pour the heavy cream into the pan with the melted butter, keep stirring. Allowing the liquid to slightly thicken, simmer for 5 minutes.
As you gradually incorporate the grated Parmesan cheese into the sauce, keep stirring so that it completely melts and the sauce thickens and creams.
To suit your tastes, season the sauce with salt and black pepper.
Make sure the cooked fettuccine pasta is thoroughly covered with Alfredo sauce before tossing it in.
Garnish with more Parmesan cheese and freshly ground black pepper before serving hot.