Separate the yolks from the whites of 3 of the eggs. Set aside the whites for another recipe. Add the remaining whole egg to the yolks and whisk well.
4 large eggs
In a large saucepan, whisk together the sugar, flour, and salt. Whisk in the milk. Cook over medium heat, stirring frequently, until it begins to bubble and thicken.
½ cup granulated sugar, 3 tablespoons all-purpose flour, ½ teaspoon kosher salt, 2½ cups whole milk
Remove from heat and pour ½ cup of the milk mixture into the eggs, whisking constantly, to temper. Whisk the egg mixture back in the saucepan and return to medium-low heat, bringing it to a gentle boil.
Cook over low heat for 2-3 minutes, whisking frequently. Remove from the stovetop and stir in the butter and vanilla. Allow the pudding to cool for 10-15 minutes.
2 tablespoons unsalted butter, 1 teaspoon pure vanilla extract
Spread a thin layer of the pudding in a shallow 9x13-inch baking pan. Place a layer of vanilla wafers on top of the pudding, then top with a layer of banana slices. Spread half of the remaining pudding over the bananas.
40 vanilla wafers, 4 ripe bananas
Continue layering wafers, bananas, and pudding, then top with crumbled wafers.
When ready to serve, add a dollop of whipped cream to each serving.
Whipped cream