Combine first 3 ingredients in top of a double boiler; add 1/2 cup milk, and m ix well. Set aside.
Scald 3 cups milk; gradually add to cornstarch mixture in top of double boiler, stirring constantly. Place over boiling water and cook, stirring constantly, until mixture is thick. Remove from heat.
Beat egg yolks in a small mixing bowl; add remaining milk. Add yolk mixture to cornstarch mixture, stirring constantly: Place over boiling water and cook, stirring constantly, until mixture is very thick. Remove from heat; let cool, stirring occasionally to prevent a crust from forming. Stir in vanilla.