In a medium saucepan, whisk together ¾ cup sugar, ¼ cup flour, and ¼ teaspoon salt until well combined.

Gradually whisk in 3 cups of milk over medium heat, stirring continuously until the mixture thickens and bubbles, about 5 minutes.

In a separate bowl, beat 3 eggs and temper them by gradually adding a small portion of the hot mixture while whisking constantly.

Return the saucepan to medium heat and stir continuously, allowing it to come to a gentle boil while thickening, about 2 more minutes.

Remove the saucepan from the heat and stir in 2 teaspoons of pure vanilla extract. Allow the mixture to cool for about 15 minutes.

In an ungreased 8x8 inch baking dish, layer around 25 vanilla wafers on the bottom. Follow with half of the sliced bananas, and pour half of the cooled pudding mixture over everything.

Add another layer of vanilla wafers and the remaining banana slices. Pour the rest of the custard over the top.

Cover the dish with plastic wrap and refrigerate for at least 4 hours, preferably overnight.

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