Chill egg whites and a small mixing bowl.
Meanwhile, in a medium saucepan, cream egg yolks with 1/2 cup sugar, salt, flour and cornstarch. Beat in milk until blended. Cook over medium-low heat, stirring with a wooden spoon, until custard coats spoon and it begins to bubble, about 10 minutes. Stir in vanilla, reduce heat and continue stirring until custard thickens, about 10 to 15 minutes. Remove from heat. Peel and cut bananas into thin slices.
Line bottom of an 8- by- 8-inch baking dish with half the vanilla wafers in a single layer. Spread sliced bananas evenly over the wafers. Spread half the custard over the bananas. Repeat layers.
Preheat oven to 375 degrees.