This dish counts on the hot pasta to cook the eggs while being tossed together before serving.  I like to pre-warm a large pasta bowl in the oven at ~200 degrees and toss everything in the warmed bowl.  That way it is ready to go straight to the table.  But the final preparation can always be done in the pot used to boil the pasta and then transferred to a serving dish.

Prepare the linguine according to the instructions on the package - they should be al dente.

While the pasta is cooking combine the yolks, cream, parmesan, zest of the whole lemon and juice of half of it, the salt and a good grind of pepper in a mixing bowl 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.

As soon as the pasta is ready, remove a cup of the cooking liquid and drain the pasta. And then, off the heat, toss it back in the pot or put it in a sufficiently preheated bowl. Throw in the butter and stir and swirl about to make sure the butter's melted and the pasta is covered 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.

Stir in the egg mixture and toss the pasta well in it, adding some of the cooking liquid if it looks a bit dry. (Only a small amount though -- you don't want a wet mess--and only after you think the sauce is incorporated.) Sprinkle over the parsley and serve.