Boil a large pot of salted water and cook the fettuccine according to package instructions until al dente.
In a saucepan, melt the butter over medium heat.
Add the heavy cream to the melted butter, stirring constantly.
Bring the mixture to a gentle simmer, then reduce the heat.
Stir in the grated Parmesan cheese gradually until melted and smooth.
Season the sauce with salt and freshly ground black pepper to taste.
Once the pasta is cooked, reserve 1/2 cup of pasta water, then drain the pasta.
Add the drained pasta to the sauce, tossing to coat evenly.
If the sauce is too thick, add reserved pasta water a little at a time until desired consistency is reached.
Plate the pasta and garnish with chopped parsley before serving.