Butter a 2 quart pyrex dish. layer bananas and vanilla wafers in the buttered dish.
Combine eggs, sugar, flour, and milk in double boiler. Cook until mixture thickens to coat a spoon (sauce will be thin).
Remove from the heat. Add butter and vanilla. Cool before pouring over layered bananas and cookies. You can serve it like this or make a meringue and put it over the pudding baking until golden.
Suggestion from Carol Watson: Add 1/4 cup creamy peanut butter when you add the butter and vanilla.
My daughter - in - law mashes the bananas instead of slicing. One recipe says to add the mashed bananas to the egg mixture while cooking; then pour over layered bananas and cookies.
This recipe is very similar to the one that my mother made. She only used the egg yolks in the pudding. When Shannon was about 4 years old, he was staying at my parents. They went to buy groceries and Shannon picked up a piece of paper from the floor and pretended to be reading a grocery list that goes like this: bananas and vanilla wafers to make a banana pudding. He loved banana pudding!