In a large heavy saucepan, combine 3/4 cup sugar and cornstarch; stir in milk until smooth. Cook and stir over medium heat until thick and bubbly; cook and stir 2 minutes more. Remove from heat.
In a bowl, beat egg yolks. Stir 1 cup hot milk mixture into yolks; return all to pan, stirring constantly. Bring to a gentle boil over medium heat; cook and stir 2 minutes longer. Remove from the heat. Stir in coconut and vanilla. Cool to lukewarm without stirring.
Pour into an ungreased 8-in. square baking dish. In a large bowl and with clean beaters, beat egg whites on medium speed until soft peaks form. Gradually beat in remaining sugar, 1 tablespoon at a time, on high until stiff peaks form. Spread over pudding, sealing to edges. Bake, uncovered, at 350° for 10-15 minutes. Serve warm.