Preheat oven to 400 degrees F.
Prepare Basic Sweet Pie Crust as directed. Roll the dough into a circle, about 1/4-inch thick. Place dough in a 9-inch pie plate, trimming and crimping the edges as the dough is gently pressed into the pan. Line the pastry with parchment paper and fill with pie weights or beans. Bake until golden brown around sides and edges, about 15 minutes. Remove parchment paper and return the crust to the oven and bake until bottom of crust is pale golden, about 5 minutes longer. Set aside on a wire rack to cool.
In a nonstick 1-quart saucepan, combine 3/4 cup sugar and 2 3/4 cups milk together. Bring the milk to boiling point and scald the milk. In a small mixing bowl, whisk the remaining milk, egg yolks, and cornstarch together. Whisk until smooth. Temper the egg yolk mixture into the scalded milk. Bring the mixture up to a boil and cook for about 3 minutes or until the mixture is thick, stirring constantly. Remove the pan from the heat and stir in 1 cup of the flaked coconut, vanilla and butter.
Pour the filling into the prepared pie shell. Cover the pie with plastic wrap and place in the refrigerator. Chill the pie completely, about 2 hours.
Preheat oven to 350 degrees F.
Using an electric mixer, whip the egg whites until stiff with the remaining 2 tablespoons of sugar. Spread the meringue evenly over the top of the pie. Sprinkle the top with the remaining 1/3 cup coconut. Bake for about 8 to 10 minutes or until golden. Remove from the oven and cool. Alternately, top with fresh sweetened whipped cream and more toasted coconut.
Sift the flour, sugar, and salt into a large bowl. Add the butter and shortening. Rub the fats between your fingertips and thumbs, or use a pastry blender, until the mixture resembles coarse crumbs. One tablespoon at a time, work in enough ice water just until the dough comes together, being careful not to over mix.
Shape into a smooth ball of dough, flatten into a disk, and wrap in plastic wrap. Refrigerate for at least 30 minutes, and up to 2 days.