Line a 9-inch pie pan with crust and then crimp the edges decoratively. Line and partially bake the crust (see Notes). Let it cool to room temperature.

To make the filling:

Combine the sugar, cornstarch, and salt in a small bowl, and use a fork or a whisk to mix them well. In another small bowl, beat the egg yolks.

In a medium saucepan over medium heat, bring the milk almost to a boil, stirring it as it heats up and begins to steam. Scoop out about ½ cup of the hot milk, and pour it into the small bowl of beaten egg yolks, stirring well as you pour. This warms up the eggs and discourages them from curdling when they are cooked. Scrape the warmed egg yolks into the hot milk mixture on the stove and stir well.

Add the sugar-cornstarch mixture to the warm egg-and-milk mixture, and stir well to dissolve it. Continue to cook over medium heat, stirring all the while, until the mixture has thickened to about the consistency of cream and become very smooth and evenly combined. Cook for about 1 minute more, and then remove the pan from the heat.

Add 1 cup of the coconut, the butter, and vanilla. Stir to mix everything together well and until the butter has melted. Place a sheet of plastic wrap directly onto the surface of the filling, and set it aside to cool to room temperature. When the filling has cooled down, pour it into the piecrust and set aside.

To make the meringue:

Heat the oven to 350 degrees F. Beat the egg whites in a medium bowl with an electric mixer on medium speed until foamy. Increase the speed to high, and add the sugar gradually, about 2 tablespoons at a time. Beat the egg whites until they thicken and swell up into plump, shiny, soft clouds that will hold firm, curly peaks.

Scoop the meringue onto the filling, and spread it out to seal the edges to the crust. Mound it up in the middle, and sprinkle the reserved coconut over the top of the meringue. Place the pie on the middle rack of the oven and bake until the meringue is a beautiful golden brown, 10 to 15 minutes. Place the pie on a cooling rack or a folded kitchen towel and let cool to room temperature, or refrigerate and serve chilled.