Set a large pot of salted water to a boil and cook the linguine until al dente or cooked to your liking.
Meanwhile, in a large bowl, whisk together the egg yolks and whipping cream. Add in the grated Parmigiano, lemon zest, lemon juice, and parsley and season with some salt and a good amount of freshly ground black pepper.
When the pasta is cooked, turn off the heat and scoop about 1 cup of the starchy cooking liquid out of the pot and reserve for later. Drain the rest of the pasta and return it to the pot. Toss 2 to 3 tablespoons of butter onto the hot pasta until each noodle is coated with a bit of butter then pour on the lemony egg and cream mixture. Stir well to combine and slowly add some of the starchy pasta water to the pasta just to loosen up the sauce a bit, about 2 tablespoons at a time.
Serve immediately topped with some more grated parm and freshly ground black pepper.