Preheat oven to 400°F and adjust oven rack to middle position.
In the small saucepan set over medium-high heat, add the water and sugar. Bring to a vigorous boil. Once the syrup is boiling vigorously, cook for exactly 4 minutes (set a timer). The mixture should be syrupy and slightly thickened. Remove from the heat after 4 minutes and set aside. (At this time, it isn’t necessary, but I found it helpful to pour the sugar syrup into a 2-cup, heatproof, measuring cup).
½ cup water, 1 cup granulated sugar
In the bowl of a stand mixer fitted with the balloon whisk attachment, beat the reserved 4 egg whites at medium speed until frothy, about 1 minute. Add the salt and cream of tartar, and gradually increase the speed to medium-high, about 2 minutes, or until whites hold soft peaks.
¼ teaspoon kosher salt, ½ teaspoon cream of tartar
With the mixer running, slowly pour the hot syrup down the inside of the bowl and into the whites (avoid the whisk so the syrup won’t splash).
Add the vanilla and continue beating until the meringue has cooled and is very thick and still shiny, about 7-10 minutes.
½ teaspoon pure vanilla extract
Once the lemon filling is cooled and set (see above), mound the meringue over the filling and then work your way around the edge being sure the meringue butts up against the crust. Once the meringue is all around the edge of the crust, mound more meringue toward the middle, pressing down slightly to ensure there are no air pockets and the meringue completely covers the filling.
Add as much meringue as you like, then use a tablespoon or rubber spatula to create peaks all over the meringue.
Place the pie on a baking sheet (for easier handling) and bake until peaks turn golden brown with white meringue showing through.
Remove the pie to a cooling rack.
At this point, the pie is beautiful and can be left alone to cool, but… if you'd like a more dramatic presentation, use a kitchen torch to toast the meringue where wanted. Be very careful to be ready to blow out any meringue that catches fire and to go slowly. Practice makes perfect.