Prepare and chill pie dough according to recipe instructions.
Roll out chilled pie dough on a lightly floured surface into a 12” circle. Transfer to a 9” pie plate and crimp or flute the edges of the crust. Place in the freezer to chill for 15 minutes, and meanwhile preheat your oven to 375F (190C).
Remove pie plate from freezer and place on a baking sheet (to easily remove from the oven without damaging the crust). Line the pie crust with parchment paper and fill with pie weights.
Bake on the center rack of 375F (190C) oven for 15 minutes. Meanwhile, prepare egg wash by whisking together egg and water.
Remove pie plate from oven and carefully remove the parchment paper and pie weights. Pierce the bottom of the pie plate repeatedly with a fork and use a pastry brush to lightly brush the pie crust all over with prepared egg wash. Return to oven (without pie weights or paper) for 10-12 minutes, until crust is beginning to turn light golden brown.
Allow crust to cool completely before filling.
For the lemon filling
In a medium-sized, non-reactive saucepan (see note), whisk together the sugar, cornstarch, and salt, then drizzle in lemon juice while whisking. Whisk until smooth.
Add egg yolks and lemon zest and whisk until well-combined.
Gradually drizzle in water, stirring until incorporated.
Turn stovetop heat just below medium and whisk constantly until mixture begins to thicken (the whisk will leave trails in the mixture, and if you dip a spoon in the lemon mixture will coat the back of the spoon).
Remove from heat and pour through a fine mesh strainer into a heatproof bowl.
Immediately add butter, whisking in until completely incorporated.
Pour filling into cooled pie crust and set aside while you make your meringue, it’s best if the meringue is added while the filling is still warm, so I’ll usually lightly tent the pie with foil to help keep the warmth from escaping. Note that your oven should still be preheated to 375F/190C, as you will need it to toast the meringue in the next step.
For the meringue
Prepare a double boiler. I like to use my stainless steel KitchenAid mixing bowl and a medium-sized saucepan that is large enough to suspend the bowl without it touching the bottom of the pan. Make sure that the bowl is completely clean, dry, and grease-free.
In the bowl of the double boiler, whisk together sugar, cream of tartar, and salt.
Add egg whites and whisk until completely combined.
Fill the bottom of the double boiler with about 1 ½ inches of water and bring to a simmer over medium-low heat. Rest the bowl of your mixer over the simmering water (it should not be touching the water).
Whisk mixture constantly until the sugar is dissolved. You can test this by carefully (it’s hot!) rubbing a small bit between your fingers, it should be smooth and not gritty. Continue whisking until mixture reaches 160F (70C).
Remove mixing bowl from heat and dry the bottom of your bowl. Fit bowl into your stand mixer (if using a stand mixer, otherwise use an electric hand mixer for the next step).
Use the whisk attachment on medium-high speed to beat the egg white mixture to stiff peaks. Meringue should be thick, billowy, and glossy. This typically takes around 10 minutes.
Stir in vanilla extract until combined.
Immediately, gently scoop meringue over pie filling. Use your spatula or the back of a spoon to create peaks from the meringue. Place on a baking sheet and transfer to the center rack of 375F (190C) oven for 10-12 minutes, until peaks of meringue are browning.
Allow pie to cool at room temperature for at least an hour before transferring to the refrigerator to cool completely (about 4 hours) before slicing and serving. This pie is best served the day it is made or next day.