In a medium saucepan, whisk together the milk, sugar, cornstarch, and salt.
Cook over medium heat, stirring constantly, until the mixture thickens and comes to a boil.
In a separate bowl, beat the eggs and vanilla extract together.
Slowly pour the hot milk mixture into the egg mixture, whisking constantly.
Return the mixture to the saucepan and cook over low heat for 2-3 minutes, stirring constantly, until thickened.
Remove from heat and let cool for 10 minutes.
In a 9x13 inch dish, layer the vanilla wafers and sliced bananas.
Pour the pudding mixture over the top, spreading it evenly.
Cover and refrigerate for at least 2 hours, or until set.
Serve chilled and enjoy your delicious banana pudding!