Make the custard first: mix the 1 cup sugar, the flour and salt in a bowl. Pour milk into a heavy saucepan and add dry ingredients. Heat but do not boil. You need to watch this carefully.
Beat the egg yolks. Pour some of the hot milk mixture into the egg yolks and beat briefly (to incorporate without curdling). Add this to the base mixture in the pan. Bring to the boil over low heat, stirring constantly, and cook slowly until just thick enough to coat the back of a spoon when dipped into the mixture. Be very careful..It is at this point that it will scorch easily.
Add the vanilla, remove the pan from the heat and cover with plastic wrap to prevent skin forming on the surface.
Line the bottom and sides of a 9x13 inch baking pan with vanilla wafers. Put a layer of bananas, then a layer of wafers in the dish until you have used all the wafers and bananas. Then pour in the custard, completely covering the bananas and wafers.
Heat the oven to 375 degrees. Beat the egg whites until they form soft peaks, and add 2 tbls sugar and beat until stiff peaks form. Spread the meringue fully over the top of the pudding, then bake until browned, about 15 to 20 minutes. This dish is really good. You can omit the meringue and use whipped cream when serving it. Either way it is good.