Heat oven to 350 degrees. Combine sugar and cornstarch in a medium sized saucepan.
Pour in milk and whisk constantly over medium high heat until mixture is thickened and bubbly, about 8 to 10 minutes.
Separate eggs. Place yolks in a small bowl and whites in a large metal mixing bowl. Set whites aside. Beat yolks slightly with a fork. Pour in a tablespoon of hot mixture into yolks. Return to hot mixture. Cook and stir over medium high heat for 2 minutes longer.
Remove from heat. Stir in butter and the teaspoon of vanilla. Mix well. Stir in the one cup of coconut.
Pour into cooled pie shell.
For the meringue:
Beat the 3 egg whites with the 1/4 teaspoon of vanilla and the cream of tartar until stiff peaks form, about 4 to 5 minutes.
Spread over pie, being sure to seal edges with meringue. Sprinkle the 1/3 cup of flaked coconut over.
Bake at 350 degrees for 15 to 18 minutes or until meringue is nicely browned.