In a saucepan, mix milk, flour, sugar, and salt. Cook over medium heat, stirring constantly until thickened.
In a bowl, beat eggs lightly. Gradually stir in a small amount of the hot milk mixture into eggs to temper them. Then, slowly pour the egg mixture back into the saucepan, stirring constantly.
Cook over low heat, stirring constantly, until the mixture is thick enough to coat the back of a spoon. Remove from heat and stir in vanilla extract.
In a serving dish, layer vanilla wafers, followed by banana slices, and then the pudding. Repeat the layers until all ingredients are used, ending with a pudding layer.
Refrigerate for at least 4 hours, or overnight, to allow the flavors to meld and the pudding to set.
Before serving, garnish with whipped cream and additional banana slices or vanilla wafers if desired.
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