Preheat oven to 350°F.
Line the bottom of a 9x13-inch baking dish with a single layer of vanilla wafers. Add a layer of sliced bananas on top of the wafers. Repeat with remaining wafers and bananas.
Mix 1 cup sugar, flour, and salt in top of double boiler. Add milk. Cook, uncovered, until mixture thickens and comes to a soft boil. Remove from heat. Add about one cup of the hot mixture to the 4 slightly beaten egg yolks, stirring constantly. Return egg mixture to pot, and cook for about 2 minutes longer. Stir in 1 teaspoon vanilla and remove from heat. Pour hot mixture over bananas and wafers in baking dish.
In a medium mixing bowl, add 4 egg whites, 1 tablespoon sugar, and 1 teaspoon vanilla. Beat egg whites on high-speed of a mixer until stiff peaks form. Spread meringue evenly over custard. Bake until meringue slightly browns, about 15 minutes.