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

Gradually add the milk to the dry ingredients while whisking constantly.

Place the saucepan over medium heat, stirring frequently until the mixture thickens and begins to bubble, about 10 to 15 minutes.

In a separate bowl, beat the eggs and slowly add a bit of the hot pudding mixture to temper them.

Pour the egg mixture back into the saucepan, stirring constantly.

Remove the saucepan from heat and stir in the vanilla extract.

In a 9x13 inch baking dish, layer vanilla wafers, sliced bananas, and the pudding mixture.

Repeat the layers until all ingredients are used.

Cover the dish and refrigerate for at least 4 hours or overnight.