For filling, in a saucepan, combine the 1 cup sugar and cornstarch. Gradually stir in the milk. Cook and stir over medium-high heat till 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 and vanilla. Pour filling into baked piecrust.
For meringue, in a mixing bowl, beat egg whites with an electric mixer till soft peaks form (tips curl). Gradually add the 1/4 cup sugar, beating till stiff peaks form (tips stand straight)and sugar dissolves.
Immediately spread meringue over hot filling
in piecrust, carefully sealing to edge of pastry to prevent shrinkage.
Sprinkle the 1/4 cup coconut over the top.
Bake the pie in a 350° oven for 15 minutes or till golden. Cool the pie completely on a wire rack. Store in the refrigerator.