Bring a large pot of lightly salted water to a boil. Add fettucine pasta and cook for 8 to 10 minutes or until al dente; drain.
In a large frypan melt the butter and add the chopped garlic. Cook on low for about 5 minutes, stirring often, making sure not to burn the garlic.
Pour about a 1/4 cup of the cream into a small bowl. Add the egg yolk and beat together; put aside. Pour the rest of the cream into the frying pan. Increase the heat to medium-high. As the cream starts to boil, mix rapidly using a whisk. Slowly add the cream/egg mixture. You do not want the egg to curdle. Continue whisking until well blended.
Add half the Parmesan cheese and continue to mix the cream. Pour in the remaining Parmesan and the parsley, mix until smooth. Immediately remove from stove. Serve the sauce over cooked pasta.