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.