Heat your oven to 400ºF and place a rack in the upper-middle position.
In a small saucepan, stir the water and sugar together. Place on medium-high heat and bring to a vigorous boil.
Once the syrup comes to a rolling boil, cook for an additional 4 minutes. The syrup will thicken.
Remove from the heat and set aside.
Using an electric mixture on low speed, beat the egg whites until frothy, about one minute.
Add the salt and cream of tartar, beat at slow speed but gradually increase the speed to medium-high until the whites have formed soft peaks, about 2 minutes.
With the mixture running, pour the hot syrup into the whites, avoiding the moving beaters.
Add the vanilla and beat until the meringue has cooled and becomes thick and shiny about 10 minutes.
Use a spatula to mound the meringue over the filling, making sure the meringue touches the edge of the pie crust.
Bake until the meringue begins to brown on the peaks - about 6 minutes.
Allow the pie to cool on a wire rack, at room temperature, until the filling has set - at least 2 hours.