Preheat the oven to 400 degrees.
In a medium-sized bowl, combine the flour, salt, and sugar for the pie crust. Stir with a fork to combine. Add the shortening, using a fork or a pastry blender to combine the shortening with the dry ingredients.
Slowly, add a few tablespoons of the water, holding the ice back so it doesn’t spill into the bowl. Use the fork to toss the mixture, adding water a little at a time. When the mixture starts to ball up and stick together, you probably have enough water. You don’t want the dough ball to be too wet, but you want all of the dry ingredients to be moistened.
When the dough starts pulling away from the sides of the bowl, use your hands to gather the dough and shape it into a disk, pressing it together gently.
On a lightly floured surface, roll the dough into a 12-inch circle using a lightly floured rolling pin. Fold the dough gently into quarters and place it into a nine-inch pie pan. Crimp the edges. Prick it well all over with a fork and bake the pie crust for 15 to 20 minutes or until it is lightly browned.
As the pie crust is baking, you can start creating the chocolate pie filling. In a medium-sized saucepan, mix together the sugar, cocoa, and salt for the pie filling, stirring in the cornstarch.
Use a wire whisk to slowly stir in the milk. Turn the stove to medium heat and slowly bring the mixture to a low boil, whisking the whole time. Take your time because milk mixtures boil over and scorch easily.
When the mixture begins to boil consistently, whisk the whole time, and boil it for a minute. Remove the pot from the heat for a moment, but leave the stove on.
In a separate bowl, beat the egg yolks lightly with a fork. Take a ladle and scoop out a spoonful of the chocolate mixture and stir it into the egg yolks. Return the egg yolk mixture to the pot, whisking it to combine. Cook the mixture for another minute.
Remove the pot from the heat and add the butter and vanilla, stirring it until the butter melts.
When the pie crust is baked, remove it from the oven and set it aside to cool to room temperature, about 5 to 10 minutes. Turn the oven temperature up to 450 degrees.
Pour the pie filling into the crust, smoothing it with a rubber spatula.
In a large mixer bowl, add the egg whites and the cream of tartar, using an electric mixer on medium speed to combine them for about a minute. Turn the mixer speed to high and beat the egg whites until soft peaks form. One tablespoon at a time, add the sugar, beating to combine.
When all of the sugar is incorporated, spread it on top of the chocolate pie all the way to the rim, sealing it at the edges.
Place the pie on top of a baking sheet to make it easier to get it in and out of the oven. Place in the oven for about five minutes, turning the pie about halfway through to make sure it browns evenly. When the meringue is browned all over, remove the pie from the oven and place it in the refrigerator, uncovered for at least two hours to cool.
Cut into slices and serve.