Combine first 3 ingredients in a heavy 2-quart saucepan; gradually stir in milk, and cook, stirring constantly, over medium heat 3 minutes or until thickened.
Stir about one-fourth of hot milk mixture gradually into egg; add egg mixture to remaining hot milk mixture, stirring constantly. Return to a boil, and cook, stirring constantly, 1 minute or until thickened. Remove from heat; stir in coconut and vanilla. Place heavy-duty plastic wrap directly on warm filling. Cool completely; chill 1 hour.