Combine 1 cup plus 2 tablespoons sugar and flour in top of a double boiler; add milk, and place over boiling water. Cook, stirring constantly, until thickened. Cover, and cook 15 minutes. Add egg yolks; cook 2 minutes, stirring constantly. Remove from heat, and stir in vanilla.
Arrange half of vanilla wafers in a lightly greased 13- x 9- x 2- inch baking dish; top with half of bananas and half of pudding. Repeat layers.
Beat egg whites (at room temperature) until soft peaks form. Gradually add remaining sugar to egg whites, 1 tablespoon at a time, beating until stiff peaks form. Spread meringue over top of pudding mixture, sealing to edge of dish. Bake at 350° for 10 minutes or until golden brown.