Adjust oven rack to middle position and preheat oven to 325°F.
Grate first and then zest lemons, reserving a tablespoon of the zest and 1/2 cup of lemon juice. Use a fine grater and cover the zest so it doesn’t get dry and it will be unnoticeable in the pie.
Divide eggs: note you’ll need six yolks and only four whites, so use another small bowl for the extra two whites. This is best done by working with one egg at a time over a small bowl or cup. Crack the egg, let the white drip into the cup, then put the yolk in one bowl and the white in another. Repeat, breaking the egg over the now empty bowl.
For the Filling:
Have all ingredients ready and within easy reach.
In a heavy medium-sized pan, mix together the sugar, cornstarch, and salt. Whisk in water and bring to a simmer, whisking constantly. When mixture starts to turn translucent, (it will still be whitish, but you’ll see the difference) working quickly and whisking vigorously, add in egg yolks, two at a time. Whisk in lemon zest, juice and butter. Return mixture to brief simmer, whisking constantly, then remove from heat. Lay sheet of plastic wrap directly on surface of filling to keep warm and prevent skin from forming.
For the Meringue:
Mix together cream of tartar and sugar, set aside.
In a small saucepan, add the tablespoon of cornstarch, then whisk in 1/3 cup water. Bring to a bare simmer and cook, whisking occasionally, until it becomes just thickened and translucent looking, 1 to 2 minutes at most. Remove from heat, transfer to a small bowl (so it doesn’t continue to cook from the heat of the pan) and let cool slightly to barely lukewarm as the eggs are being whisked.
If using stand mixer, fit it with the whisk. Beat egg whites and vanilla at medium low-speed until foamy and frothy. Turn the speed up to medium-high and add, a tablespoon at a time, the cream of tartar and sugar mixture. Beat until incorporated (it won’t feel grainy when you run a bit between your fingers) and the mixture forms soft, billowy mounds.
While continuing to whip, add the cooked cornstarch mixture, about a tablespoon at a time. As it’s added, place it between the beaters and the side of the bowl. Continue to beat until stiff, glossy peaks form, about two to three minutes longer.
If filling is not still hot, during the last minutes of beating the egg whites, remove plastic and return to very low heat for just a moment or two to warm.
Pour warm filling into cooled pre-baked pie crust. Working quickly, dollop meringue in small mounds across the hot pie filling. Using rubber spatula, immediately distribute meringue evenly around edge first and then the then center of pie, attaching meringue to pie crust to prevent shrinking. Top off with any remaining meringue.
Using the back of spoon, create attractive swirls and peaks in the meringue. (I personally like to use the spoon to make small “scallops” with only a very few peaks which prevent the peaks from over baking before the rest is nicely browned.) Bake until meringue is light golden brown, about 20 minutes.
Cool to room temperature on a rack (at least two hours, Cook’s says, but count on three & half). This pie is at it’s best the same day.
Have all ingredients ready; this is most definitely not a measure and ready it as you go recipe. Timing is critical.