Here is the original restaurant in Rome, where the dish was invented:
They sort of have the recipe online. It lacks the precise measurements and detailed instructions to which many folks are accustomed. The translation’s also a bit funny, like it says “pasta egg” instead of “egg pasta”, etc.
I’ve never been to this restaurant – apparently it is a bit on the expensive side – but I am told that they are famous for serving your meal with a golden fork, and that the fettuccine alfredo is unlike anything we have in the States: light, fluffy, low cal (j/k), etc. etc.