Make sure your pie crust is baked and cooled in an 8-9" pie plate.
Preheat oven to 300°F.
Whisk water, sugar, cornstarch, salt, lemon juice, and lemon zest in a medium saucepan. Place over medium-low heat and cook, stirring often, until it’s thick and bubbly.
Place egg yolks into a medium sized bowl. Whisk them gently. Once the lemon mixture is thick and bubbly, carefully pour about half the lemon mixture into the egg yolks, whisking constantly, then place the egg mixture back into the pan with the remaining lemon mixture, continuing to whisk. You want to avoid scrambling the eggs. Bring to a gentle boil, then cook for 2 minutes. Remove from heat and stir in the butter until melted.
Pour mixture into the prepared pie crust. (If so inclined, strain it into the pie through a mesh strainer to remove any egg bits.) Cover with plastic wrap while you prepare the meringue.
Place egg whites, cream of tartar, and vanilla in the bowl of a stand mixer fitted with the whisk attachment (or you can use a large bowl with a hand mixer). Beat on high speed until soft peaks form (if you remove the beaters the tips curl slightly) and then continue mixing while gradually adding the granulated sugar. Continue mixing until stiff peaks form (they’ll be glossy and stand straight).
Spread the meringue on the top of the lemon mixture in decorative peaks, being sure that the meringue touches the crust and no lemon shows through. Bake about 30 minutes or until the meringue is browned. Cool at room temperature for one hour, then chill at least 5 hours before slicing.
The pie will last a day or two in the refrigerator but tastes better day one.