Prepare Baked Pastry Shell. Cool. For filling, in a saucepan, combine the 1 cup sugar and the cornstarch. Gradually stir in the milk. Cook and stir over medium-high heat until mixture is thickened and bubbly. Remove the saucepan from heat.
In a bowl, beat the egg yolks with a fork. Gradually stir about 1 cup of the hot filling into yolks. Return all to saucepan. Bring to a gentle boil. Cook and stir for 2 minutes more.
Remove mixture from the heat. Stir in the 3/4 cup coconut, the butter or margarine, and vanilla.
Pour filling into baked pastry shell.
For meringue, in a mixing bowl, beat egg whites with an electric mixer until soft peaks form (tips curl). Gradually add the 1/4 cup sugar, beating until stiff peaks form (tips stand straight) and sugar dissolves.
Immediately spread meringue over hot filling in pastry shell, carefully sealing to edge of pastry to prevent shrinkage. Sprinkle the 1/4 cup coconut over the top.
Bake the pie in a 350 degree F oven for 15 minutes or until golden. Cool the pie completely on a wire rack. Store in the refrigerator. Makes 8 servings.