In a medium saucepan, whisk together the sugar, cornstarch, and salt.

Gradually whisk in the whole milk until smooth. Cook over medium heat, stirring constantly, until the mixture thickens and comes to a gentle boil. Boil for 1 minute, stirring constantly.

In a small bowl, whisk the egg yolks. Gradually temper the egg yolks by slowly whisking about 1 cup of the hot milk mixture into them. Pour the tempered egg yolk mixture back into the saucepan with the remaining milk mixture. Cook over medium-low heat, stirring constantly, until thickened, about 2-3 minutes. Do not boil.

Remove from heat and stir in the vanilla extract and butter until the butter is melted and incorporated.

Pour the custard into a clean bowl. Cover the surface directly with plastic wrap to prevent a skin from forming. Let cool at room temperature for 30 minutes, then refrigerate for at least 2 hours, or until thoroughly chilled.

To assemble the pudding, spread a layer of vanilla wafers in the bottom of a 9x13 inch baking dish. Top with a layer of sliced bananas. Spoon a layer of chilled custard over the bananas. Repeat layers of wafers, bananas, and custard, ending with a layer of custard.

Cover the dish with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow the wafers to soften.