Cook rice until tender and set aside. Mix flour or cornstarch with 2/3 cup sugar and salt. Separate eggs and set whites aside (for meringue). Beat yolks with a fork and mix with milk. Mix with cornstarch and sugar mixture and cook over medium heat until boiling. Boil while stirring for 1 minute. Remove from heat and stir in butter and 2 teaspoons of vanilla. Sweeten rice to taste and mix with pudding.
Meringue: Whip egg whites with cream of tartar until foamy. Sprinkle 1/4 cup sugar on while whipping, until swirls are thick. Add 1/2 teaspoon vanilla.
Pour pudding and rice mixture in baking dish and spread with meringue. Brown in preheated oven at 350 degrees F.