In a medium saucepan, whisk together sugar, flour, and salt. Gradually stir in the milk while cooking over medium heat, stirring continuously until the mixture thickens and bubbles, about 10-12 minutes.

Reduce the heat to low and cook the custard for an additional 2 minutes. In a small bowl, whisk the eggs. Temper the eggs, then pour back into the saucepan, and cook for 2 more minutes until thickened.

Remove from heat and stir in vanilla extract. Let cool for about 15 minutes, stirring occasionally.

In an 8x8 inch square pan, place about 25 vanilla wafers as the first layer. Follow with half of the banana slices and pour half of the pudding over them. Repeat layers.

Cover with plastic wrap, refrigerate for at least 4 hours or overnight for best results.

Before serving, crush any remaining vanilla wafers and sprinkle on top.

Serve cold, optionally garnished with fresh banana slices or whipped cream.