Preheat the oven to 350°F (180°C).
Roll out the pie crust and line a 9-inch (23cm) pie tin with it. Bake the crust for 10 minutes.
While the crust is baking, prepare the filling: In a saucepan, combine the apples and water and cook over medium-low heat for about 10 minutes, or until the apples are tender.
Remove the apples from the heat and whisk in the egg yolks, sugar, and lemon juice.
Fill the partially baked crust with the apple mixture and bake for about 30 more minutes, or until the filling is set. Let cool completely.
Once the pie is completely cool, make the meringue topping: in the top of a double boiler, combine the egg white, sugar, and cream of tartar and heat gently, stirring constantly, until the sugar is melted.
Remove from the heat and beat with an electric mixer until stiff, glossy peaks are formed.
Dollop and swirl the meringue topping on the pie. Toast the top with a butane kitchen torch. (If you don’t have a torch, you can place the pie under the broiler for a minute or two, but watch it very carefully as it can burn very quickly.)
This pie can be stored without the topping, loosely covered in the refrigerator, for up to 2 days. Once the meringue topping has been placed on the pie, it is best served the day it is made, but can be stored in the refrigerator for up to one day.