Fill just about the biggest pot you have with water and bring to a boil. When friends are coming for lunch, get the water heated to boiling point before they arrive, otherwise you end up nervously hanging around waiting for a watched pot to boil while your supposedly quick lunch gets later and later. Bring the water to the boil, cover and turn off burner.
I tend to leave the addition of salt until the water comes to a boil a second time. But whichever way you do it, add quite a bit of salt. When the bubbling's encouragingly fierce, put in the pasta. I often put the lid on for a moment or so just to let the pasta get back to the boil, but don't turn your back on it, and give it a good stir with a pasta fork or whatever to avoid even the suspicion of stickiness, once you've removed the lid.
Then get on with the sauce, making sure you've set your timer for about a minute or so less than the time specified on the package of pasta.
In a bowl, add the yolks, cream, Parmesan, zest of the whole lemon and juice of half of it, the salt and good grind of pepper, and beat with a fork. You don't want it fluffy, just combined. Taste. If you want it more lemony, then of course add more juice.
When the timer goes off, taste to judge how near the pasta is to being ready. I recommend that you hover by the stove so you don't miss that point. Don't be too hasty, though. Everyone is so keen to cook their pasta properly al dente that sometimes the pasta is actually not cooked enough. You want absolutely no chalkiness here. And linguine (or at least I find it so) tend not to run over into soggy overcookedness quite as quickly as other long pasta. This makes sense, of course, as the strands of "little tongues" are dense than the flat ribbon shapes.
Anyway, as soon as the pasta looks ready, remove a cup of the cooking liquid, drain the pasta, and then, off the heat, toss it back in the pot or put it in an efficiently preheated bowl, throw in the butter, and stir and swirl about to make sure the butter's melted and the pasta covered by it all over. Each strand will be only mutely gleaming, as there's not much butter and quite a bit of pasta. If you want to add more, then do; good butter is the best flavoring, best texture, best mood enhancer there is.
When you're satisfied the pasta's covered with its soft slip of butter, then stir in the egg mixture and turn the pasta well in it, adding some of the cooking liquid if it looks a bit dry (only 2 tablespoons or so - you don't want a wet mess - and only after you think the sauce is incorporated). Sprinkle over the parsley and serve now, now, now.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.