Well if I knew.... It just always splits a little and is grainier than I prefer. Or too thick. Might just be I prefer it processed from a jar though. I'm not too proud to admit one of the only things I like at olive garden is the dipping side of Alfredo that seems a bit smoky.
I've always just made it with heavy cream, butter, and a combo of Parmesan and Pecorino Romano. I've seen where you can add an egg yolk to help emulsify some, but haven't tried it.
Start reducing cream, add cold butter, toss in cheese in portions, constantly stirring. Add pasta, and doesn't have to be thoroughly dry. Reserve some pasta water, or splash with a little more cream for desired consistency.
I think a lot of it is just the right temp and constantly moving so you can make that emulsification happen. I guess if you were going to add the egg yolk you do it when you maybe have the butter, I don't remember but you would need to temper it first.
But send me what pasta or pasta water is going to help emulsify it some because of the starches.
I guess when I was learning to make it I broke the sauce a couple of times before I sort of got it down and at this point I just kind of know what to do, and if you do it enough you get a knack for it.
I don't make it from scratch very often any longer, not that it's hard, but I'll take a jar of the pre-made and then add more cream less butter and then whatever cheese I want. I find that if I'm putting together a whole bunch of other stuff and if I'm bouncing back and forth, the stabilizers in the pre-made stuff keep the sauce from breaking if I'm gone too long. I can literally shut it off and then turn it back on just to heat right before dinner, normally because I might be out on the grill with whatever protein. I honestly can't tell the difference that much between straight up scratch versus the doctored version.
Sometimes all grate some lemons zest or maybe throw a sprig or two of time or a bit of fresh basil in, and usually always have parsley. You can always add garlic to, but just soften that with a nob of butter and then add your cream. Can always splash a quarter cup of white wine in and cook the alcohol off when you're doing the garlic if you want additional flavor. Probably not Alfredo at that point but whatever, it tastes good.
I know the true blue traditional Italian doesn't use cream and it's literally just butter, cheese, and pasta water I think. Cream is the Americanized version.