My grandfather told me he learned to make this from Alfredo himself. He also said he personally visited the queen of England and dated Kathryn Hepburn and told her to quit acting and marry him because she'd never make it in Hollywood, so maybe take the origin of this with a grain of salt...However he learned how to make this, the recipe has been a family secret for at least three generations and is the best fettuccine Alfredo I've ever had. It's also super easy, although the measurements are along the lines of "add until the spirit of your ancestors tells you 'that's enough'" rather than being super accurate.
Ingredients:
1 lb fettuccine noodles
Salt for the pasta water
1 stick of butter
1 egg yolk
1 pint of heavy cream
About 16 oz of grated Parmesan cheese (if you can get fresh, that's best, but I often just use the one from the local grocery store as we don't have Italian delis where I currently live - also, I like the combo Parmesan and Romano cheese as well)
Start by boiling a pot of water with some salt added. I think a few teaspoons of salt? Or maybe a tablespoon? You want to add some flavor to the pasta, but not make it overwhelmingly salty.
Once the water is boiling, add 1 lb of fettuccine noodles. Do not break them to make them fit in the pot. No real Italian does that. I've seen lots of social media videos that showcase Italians' responses to people who break the pasta to put it in the pot. Stir it about every 30 seconds to a minute at the beginning until it's all under water. Then stir it every minute or two to make sure the noodles don't stick together. Cook to al dente, which means cooked with a slightly firm center. This is one of the things that my ancestors whisper to me, which has apparently also been inherited by at least one of my children. Check the box of pasta if you want more specific directions and make sure to factor in your altitude. Things take longer to cook at higher altitudes.
While the pasta is cooking, combine the egg yolk with some of the cream (maybe 1/3 cup) and mix it together. This is so the egg yolk can spread through the pasta instead of cooking into fried egg bits.
Drain the pasta, but don't shake it to get all the water out. Leave a little of the water on the noodles to make the sauce creamier. Return it to the pot you cooked it in, but take the pot off the stove. Proceed to the next step quickly - don't let the pasta cool.
Cut the stick of butter into slices and put them into the pasta to melt. Stir the melted butter into the pasta. Add the yolk/cream mixture and stir to coat all the noodles. Pour in about half the container of cream and mix to coat the pasta. Add about half the container of grated cheese and stir to combine. Add more cheese if you want it to have more flavor and more cream if it's too thick. We like lots of sauce, so I usually end up adding about one 16 oz container of cream and about 16 oz of shredded cheese per lb of pasta. Serve immediately.